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Short Answer Type Questions

Q1. What is ‘Depreciation’?

ANSWER: Depreciation means fall in book value of depreciable fixed asset because o

1. wear and tear of the asset
2. passage/efflux of time
3. obsolescence
4. accident

A machinery costing ₹ 1,00,000 and its useful life is 10 years; so, depreciation is calculated as:
Annual Depreciation per annum
= Cost of Asset-Estimated Scrap Value/Expected or Estimated life of Asset
= 100000/10 = ₹ 10,000

Q2. State briefly the need for providing depreciation.

ANSWER: The needs for providing depreciation are given below.

1. To ascertain the correct profit or loss: Correct profit or loss can be ascertained when all the expenses and losses incurred for earning revenues are charged to Profit and Loss Account. Assets are used for earning revenues and its cost is charged in form of depreciation from Profit and Loss Account.
2. To show true and fair view of financial statements: If depreciation is not charged, assets will be shown at higher value than their actual value in the balance sheet. Consequently, the balance sheet will not reflect true and fair view of financial statements.
3. For ascertaining the accurate cost of production: Depreciation on the assets, which are engaged in production, is included in the cost of production. If depreciation is not charged, the cost of production is underestimated, which will lead to low selling price and thus leads to low profit.
4. To provide funds for replacement of assets: Unlike other expenses, depreciation is non cash expense. So, the amount of depreciation debited to the profit and loss account will be retained in the business. These funds will be available for replacement of fixed assets when its useful life ends.
5. To meet the legal requirement: To comply with the provisions of the Companies Act and Income Tax Act, it is necessary to charge depreciation.

Q3. What are the causes of depreciation?
ANSWER:

1. Use of asset: Because of constant use of the fixed assets there exists a normal wear and tear which leads to fall in the value of the assets.
2. Passage of time: Whether assets are used or not, with the passage of time, its effective life will decrease.
3. Obsolescence: Because of new technologies, innovations and inventions, assets purchased currently may become outdated later which leads to the obsolescence of fixed assets.
4. Accident: An asset may lose its value due to mishaps such as a fire accident, theft or by natural calamities and they are permanent in nature.

Q4. Explain basic factors affecting the amount of depreciation.
ANSWER:

1. Original cost of asset: The total cost of an asset is taken into consideration for ascertaining the amount of depreciation. The total cost of an asset include all expenses incurred up to the point the asset is ready for use like freight expenses and installation charges.
   Total Cost= Purchase Price+ Freight Expenses+ Installation Charges.
2. Estimated useful life: Every asset has its useful life other than its physical life in terms of number of years and units used by a business. The asset may exist physically but may not be able to produce the goods at a reasonable cost. For example, an asset is likely to lose its useful value within 15years, its useful life, i.e., life for purpose of accounting should be considered as only 15 years
3. Estimated scrap value: It is estimated as the net realisable value of an asset at the end of its useful life. It is deducted from the total cost of an asset and the difference is written off over the useful life of the asset. For example, Furniture acquired at ₹ 1,30,000, its useful life is estimated to be 10 years and it is estimated scrap value ₹ 10,000.
   Depreciation per annum= 1,30,000-10,000/10 years= 12,000

Q5. Distinguish between straight line method and written down value method of calculating depreciation.
ANSWER:

Straight Line Method	Written Down Value Method
Depreciation is calculated on the original cost of an asset.	Depreciation is calculated on the reducing balance, i.e., the book value of an asset.
Equal amount of depreciation is charged each year over the useful life of the asset.	Diminishing amount of depreciation is charged each year over the useful life of the asset.
Book value of the asset becomes zero at the end of its effective life.	Book value of the asset can never be zero.
It is suitable for the assets such as patents, copyright, land and buildings which have lesser possibility of obsolescence and lesser repair charges.	It is suitable for assets which needs more repair in the later years such as plant and machinery and car.
As depreciation remains same over the years but repair cost increases in the later years, there will be unequal effect over the life of the asset.	As depreciation cost is high and repairs are less in the initial years but in the latter years the repair costs increase and depreciation cost decreases, there will be equal effect over the life of the asset.
It is not recognised under the income tax act.	It is recognised under the income tax act.

Q6. “In case of a long term asset, repair and maintenance expenses are expected to rise in later years than in earlier year”. Which method is suitable for charging depreciation if the management does not want to increase burden on profits and loss account on account of depreciation and repair.
ANSWER:
The written down value method is most appropriate to overcome the burden of the profit and loss account because of high depreciation and repair costs over the years of the asset. The cost of depreciation reduces and the repair and maintenance expenses increase over the yea₹ However, the entire burden will not get ease to the management.

Q7. What are the effects of depreciation on profit and loss account and balance sheet?
ANSWER:
The effects of depreciation on Profit and Loss Account are as follows:

1. An increase in depreciation will be debited in the profit and loss account which reduces net profit.
2. Hence total expenses increase which leads to an excess of debit over credit balance.

The effects of depreciation on Balance Sheet are as follows:

1. The original cost or book value of the concerned asset gets reduced.
2. The overall balance of asset’s column in the balance sheet gets reduced.

Q8. Distinguish between ‘provision’ and ‘reserve’.
ANSWER:

Provision	Reserve
It is charge against profit.	It is an appropriation of profit.
It is created to meet a specific liability or contingencies.	It is made for strengthening the financial position of the business. Some reserves are also mandatory under law.
It is recorded on the debit side of profit and loss account.	It is recorded on the credit side of the profit and loss appropriation account.
It can be shown either (i) by way of deduction from the item on the assets side for which it is created, or (ii) in the liabilities side along with the current liabilities.	It is shown on the liabilities side after capital.
It cannot be utilized for dividend distribution.	It can be utilized for dividend distribution.
It is never invested outside the business.	It can be invested outside the business.
It reduces net profits.	It reduces only divisible profit.

Q9. Give four examples each of ‘provision’ and ‘reserves’.
ANSWER:
Four examples of provision are given below.

1. Provision for bad and doubtful debts
2. Provision for discount on debtors
3. Provision for depreciation
4. Provision for tax

Four examples of reserve are given below.

1. General reserve
2. Capital redemption reserve
3. Dividend equalisation reserve
4. Debenture redemption reserve

Q10. Distinguish between ‘revenue reserve’ and ‘capital reserve’.
ANSWER:

Revenue Reserve	Capital Reserve
It is formed out of revenue profit which is earned from normal activities of business operations.	It is formed out of capital profit which is a gain from other than normal activities of business operations, such as sale of fixed assets.
It can be used for distribution of dividend.	It cannot be used for distribution of dividend.
It is created for increasing the financial position of the business.	It is created for the purpose of the Companies Act.

Q11. Give four examples each of ‘revenue reserve’ and ‘capital reserve’.
ANSWER:
Examples of revenue reserve are as follows:

1. General reserve
2. Investment equalisation reserve
3. Dividend equalisation reserve
4. Debenture reserve

Examples of capital reserve are as follows:

1. Issues of shares at premium
2. Profit on forfeiture of shares
3. Profit on sale of fixed assets
4. Profit on redemption of debentures

Q12. Distinguish between ‘general reserve’ and ‘specific reserve’.
ANSWER:

Specific Reserve	General Reserve
It is created for specific purpose.	It is not created for specific purpose.
It is not available for any future contingencies or expansion of business. It is utilised only for that purpose for which it is created.	It is available for any future contingencies or expansion of business. It strengthens the financial position.
Dividend equalisation reserve, debenture redemption reserve, development rebate reserves.	Contingency reserve and general reserve

Q13. Explain the concept of ‘secret reserve’.
ANSWER:
Secret reserves are created by overstating liabilities or understating assets which are not shown in the balance sheet. This will reduce tax liabilities, because the liabilities are overstated. It is created by management to avoid competition by reducing profit. Creation of secret reserve is not allowed by Companies Act, 1956 which requires full disclosure of all material facts and accounting policies while preparing final statements.

Long Answer Type Questions

Q1. Explain the concept of depreciation. What is the need for charging depreciation and what are the causes of depreciation?
Solution:
Depreciation means fall in book value of depreciable fixed asset because of

1. wear and tear of the asset,
2. passage/efflux of time,
3. obsolescence, or
4. accident.

The need for providing depreciation is:

1. To ascertain the correct profit: Correct profit or loss can be ascertained when all the expenses and losses incurred for earning revenues are charged to Profit and Loss Account. Assets are used for earning revenues and its cost is charged in form of depreciation from Profit and Loss Account.
2. To show true and fair view of the financial position: If depreciation is not charged, assets will be shown at higher value than their actual value in the balance sheet. Consequently, the balance sheet will not reflect true and fair view of financial statements.
3. To retain, out of profit, funds for replacement: Unlike other expenses, depreciation is non cash expense. So, the amount of depreciation debited to the profit and loss account will be retained in the business. These funds will be available for replacement of fixed assets when its useful life ends.
4. To ascertain correct cost of production: Depreciation on the assets, which are engaged in production, is included in the cost of production. If depreciation is not charged, the cost of production is underestimated, which will lead to low selling price and thus leads to low profit.
5. To meet the legal requirement: To comply with the provisions of the Companies Act and Income Tax Act, it is necessary to charge depreciation.

The causes of depreciation are as stated below:

1. Use of Asset i.e., wear and tear: Due to constant use of the fixed assets there exist a normal wear and tear that leads to fall in the value of the assets.
2. Passage/Efflux of Time: Whether assets are used or not, with the passage of time, its effective life will decrease.
3. Obsolescence: Due to new technologies, innovations and inventions, assets purchased today may become outdated by tomorrow which leads to the obsolescence of fixed assets.
4. Accidents: An asset may lose its value due to mishaps such as a fire accident, theft or by natural calamities and they are permanent in nature.

Q2. Discuss in detail the straight line method and written down value method of depreciation. Distinguish between the two and also give situations where they are useful.
Solution:
The two methods of depreciation are

1. Fixed percentage on original cost or straight line method
2. Fixed percentage on diminishing balance or written down value method

Straight Line Method
According to this method, a fixed and equal amount is charged as depreciation for every accounting period during the life time of an asset. This method is based on the assumption of equal usage of time over asset’s entire useful life. Hence, the amount of depreciation is same from period to period over the life of the asset.

Depreciation amount can be calculated by using the following formula:

• If the asset has a residual value at the end of its useful life, the amount to be written of every year is as follows:
  Depreciation = Cost of asset – Estimated net residual value / No. of years of expected life
• If the annual depreciation amount is given then we can calculate the rate of depreciation as follows:
  Rate of depreciation = Annual depreciation amount / Cost of asset * 100

Advantages of Straight Line Method

1. Simple to calculate the depreciation amount
2. Assets can be depreciated up to the estimated scrap value
3. Easy to understand the amount of depreciation
4. Every year, the same amount of depreciation is debited to profit and loss account, and hence the effect on profit and loss account will remain the same.

Disadvantages of Straight Line Method

1. Interest on capital invested in assets is not provided in this method.
2. Over the years, the work efficiency of assets decreases and repair expenses increases. Therefore, there is burden on the profit and loss account.
3. Book value of the assets becomes zero but still the assets are used in the business.

Written Down Value Method
In this method depreciation is charged on the book value of the asset and the amount of depreciation reduces year after year. It implies that a fixed rate on the written down value of the asset is charged as depreciation every year over the expected useful life of the asset. The rate of depreciation is applicable to the book value but not to the cost of asset.

Rate of depreciation can be ascertained on the basis of cost, scrap value and useful life of the asset as follows:

Where, R is the rate of depreciation in percent, n is the useful life of the asset; S is the scrap value at the end of useful life and C is the cost of the asset.

Advantages of Written Down Value Method

1. The profit and loss account of depreciation and repair expenses has same weightage throughout the useful life of asset because depreciation decreases with an increase in repair expenses.
2. Since the benefits from asset keep on decreasing, the cost of asset is allocated rationally.
3. This method is most favorable for those assets which require increased repairs and maintenance expenses over the years.
4. This method is widely accepted under the Income Tax Act.

Disadvantages of Written Down Value Method

1. The value of assets can never be zero even though it is discarded.
2. In this method, it is difficult to calculate depreciation.
3. There is no provision of interest on capital invested in use of assets.

Difference between Straight Line and Written Down Value Method

Straight Line Method	Written Down Value Method
Depreciation is calculated on the original cost of fixed asset	Depreciation is calculated on the book value (i.e. original cost less depreciation) of fixed asset
Amount of depreciation remains constant for all years	Amount of depreciation keeps on decreasing year after year
At the end of the useful life of an asset, the balance in the asset account will reduce to zero	At the end of the useful life of an asset, the balance in the asset account will not reduce to zero
It is not accepted by Income Tax Law	It is accepted by Income Tax Law
It is suitable for assets which get completely depreciated on the account of expiry of its useful life	It is suitable for assets which require more and more repairs in the later stage of its useful life
Rate of depreciation is easy to calculate	Rate of depreciation is difficult to calculate

Q3. Describe in detail two methods of recording depreciation. Also give the necessary journal entries.
Solution:
The two methods of recording depreciation are as follows:
1. When Depreciation is Charged or Credited to the Assets Account
In this method, depreciation is deducted from the asset value and charged (debited) to profit and loss account. Hence the asset value is reduced by the amount of depreciation.

In the Balance sheet, asset appears at its written down value which is cost less depreciation charged till date. In this method, the original cost of an asset and the total amount of depreciation which has been charged cannot ascertain from this balance sheet.
2. When Depreciation is Credited to Provision for Depreciation Account
In this method, depreciation is credited to the provision for depreciation account or accumulated depreciation account every year. Depreciation is accumulated in a separate account instead of adjusting into the asset account at the end of each accounting period. In the balance sheet, the asset will continue to appear at the original cost every year. Thus, the balance sheet shows the original cost of the asset and the total amount of depreciation charged on asset.

Q4. Explain determinants of the amount of depreciation.
Solution:

1. Historical (Original) Cost of the Asset: The total cost of an asset is taken into consideration for ascertaining the amount of depreciation. The total cost of an asset include all expenses incurred up to the point the asset is ready for use like freight expenses and installation charges.
   Total Cost =Purchase Price+ Freight Expenses+ Installation Charges.
2. Estimated Net Residual Value: It is estimated as the net realisable value of an asset at the end of its useful life. It is deducted from the total cost of an asset and the difference is written off over the useful life of the asset. For example, Furniture acquired at Rs.1,30,000, its useful life is estimated to be 10 years and it is estimated scrap value Rs.10,000.
   Depreciation p.a.= 1,30,000-10,000/10 Years = Rs.12,000
3. Estimated Useful Life: Every asset has its useful life other than its physical life (in terms of number of years, units, etc.), used by a business. The asset may exist physically but may not be able to produce the goods at a reasonable cost. For example, an asset is likely to lose its useful value within 15 years, its useful life, i.e., life for purpose of accounting should be considered as only 15 years.

Q5. Name and explain different types of reserves in details.
Solution:
Types of Reserves:

1. Revenue Reserve: It is an amount set aside out of revenue profits for distribution of dividends. For example, general reserve, investment fluctuation fund, capital reserve and workmen compensation fund. It is not a charge against profit but it is appropriation of profit shown in the profit and loss account. It is beneficial for the smooth function of the business. The retention of profit in the form of reserves reduces the amount of profit to distribute among the business owners. This is further classified in to general reserve and specific reserve.
   1. General reserve means a reserve which is not maintained for specific purpose. It helps to strengthen the financial status of the business. It is also known as free reserve and contingency reserve.
   2. Specific reserve means a reserve which is maintained for specific purpose. For example, dividend equalisation reserve is created to maintain dividend rate. This reserve amount is utilised to maintain the rate dividend in the year of low profit. Likewise, the workmen compensation fund is maintained to provide claims of the workers, investment fluctuation fund is used at times of decline in the value of investment and debenture redemption reserve is used to provide funds for redemption of debentures.
2. Capital Reserve: It is an amount set aside out of capital profits which is not available for distribution as dividend among the shareholders. It is used for writing capital losses/issue of bonus share in a company. Examples of capital reserves are
   • Profit prior to incorporation
   • Premium on issue of shares or debentures
   • Profit on redemption of debenture
   • Profit on forfeiture of share
   • Profit on sale of fixed assets
   • Capital redemption reserve
   • Profit on revaluation of fixed assets and liabilities

Q6. What are ‘provisions’? How are they created? Give accounting treatment in case of provision for doubtful Debts.
Solution:
Provision is an amount which is set aside by charging it to profit for the purpose of providing for any known liability or uncertain loss or expense. The amount of which cannot be determined with certainty is also referred to as provision. Few examples are provision for depreciation, provision for doubtful debts and provision for discount on bad debtors.
The main objective of provision is to account all expenses and losses. Through the creation of provision account, the amount of liability, losses and expenses are estimated and accounted for the accounting period. Therefore, the true profit and loss is ascertained, liabilities and assets are presented with correct values.
Importance of Provision:

1. To meet anticipated losses and liabilities: Provision is created to meet the anticipated losses and liabilities such as provision for doubtful debts, provision for discount on debtors and provision for taxation.
2. To meet known losses and liabilities: Provision is created to meet known losses and liabilities such as provision for repairs and renewals.
3. To present correct financial statements: To present a true and fair view of profit and financial statement, the business must maintain provision for known liabilities and losses.

Therefore, provision is necessarily to be created to ascertain the current income or profit. Also, it is considered as a charge against revenue or profits.
Accounting Treatment
Provision is a charge against the profit which is debited in the profit and loss account. In the balance sheet, the amount of provision may be shown on the asset side by deducting from the relevant asset or on the liability side along with the current liabilities.

1. Treatment on asset side- Provision for doubtful debts is deducted from the amount of sundry debtors and the provision for depreciation is deducted from the relevant asset.
2. Treatment on liability side- Provision for repairs and charges are shown along with the current liabilities.

Short Answer Type Questions

Q1. State the meaning of a Trial Balance.
Solution: Trial balance is a statement prepared to check the arithmetical accuracy of transactions recorded in the journal, posted into the ledger and balanced in the ledger accounts.  The balance of ledger accounts shows the difference between the total of the debit items and credit items in an account. Personal, real and nominal accounts are considered for preparing the trial balance. Generally, it is prepared at the end of an accounting year. However, it may be prepared at the end of any chosen period, which may be monthly, quarterly, half yearly or annually depending upon when it is required. It helps in the preparation of the financial statements.

Q2. Give two examples of errors of principle?
Solution: Generally accepted accounting principles are to be followed to record the accounting entries. When accounting entries are recorded in contravention of accounting principles, it is known as an error of principle.

1. Wages paid for installation of new machinery debited to wages account:
2. Wages paid for installation of new machinery is a capital expenditure and accordingly machinery account should have been debited. But, here it is treated as revenue expenditure and is debited to wages account. Thus, it violates the accounting principle.
3. Amount spent on repair of building debited to machinery account: Expense on repair is revenue expenditure and not a capital expenditure. The amount should have been debited to repairs account and to the machinery account which is a capital account. Thus, it violates the accounting principle.

Q3. Give two examples of errors of commission?
Solution: Errors of commission are committed because of wrong recording, wrong posting, wrong balancing and wrong casting of subsidiary books. Such errors affect the accuracy of the trial balance.

1. Cash received from a creditor worth Rs.5,000 is recorded in the cash book as Rs.500.
   The transaction is recorded in the cashbook as Rs.500 instead of Rs.5,000. This is an error because of the wrong recording of amount in the cash book.
2. Amount received from Arun Rs.2,000, is wrongly posted in Tarun’s account.
   In this transaction, Tarun’s A/c is credited instead of Arun’s A/c. This is referred to as an error of wrong posting of transactions.

Q4. What are the methods of preparing trial balance?
Solution: A trial balance can be prepared in the following three ways :

1. Totals Method: In this method, the total of the debit and the credit side of the ledger is determined and presented separately in the trial balance. The total of both the sides should match as the accounts are based on double entry system.
2. Balances Method: In this method, the balances of all ledger accounts are presented in their respective debit and credit columns of the trial balance. The total of both the sides should match as the accounts are based on double entry system and this method of preparing a trial balance is widely used because it helps in the preparation of financial statements.
3. Totals-cum-balances Method: This method is a blend of the totals and balances method. This method has four columns. The first two columns are to write the totals of the debits and credits of the various accounts and the other two columns are to write the debit or the credit balances of these accounts. This method is time consuming, and hence are not used widely.

Q5. What are the steps taken by an accountant to locate the errors in the trial balance?
Solution: Steps to identify the errors:

1. Recast the totals of the debit and credit columns of the trial balance.
2. Compare each account head and its amount appearing in the trial balance with that of the ledger to detect any difference in amount or omission of any account.
3. Compare the trial balance of the current year with that of the previous year to check the additions or deletions to any accounts and to verify if there is any unexplained difference in amounts.
4. Re-check the correctness of balances of individual accounts in their respective ledgers.
5. Re-check the accuracy of the postings in individual accounts from the transactions entered in the books of original entry.
6. If the difference between the debit and credit columns is of `1, `10, `100 or `1000, the casting of the subsidiary books should be re-checked.
7. If the difference between the debit and credit columns is divisible by 2, then there is a possibility that an amount equal to half the difference may have been posted to the wrong side of another ledger account.
8. The above point may also indicate a complete omission of a posting.
9. If the difference is divisible by 9, the mistake could be because of transposition of figures.
10. Still, if it is not possible to locate the errors, the difference in the trial balance for that moment is transferred to the suspense account. All the one-sided errors detected are rectified through this account.

Q6. What is a suspense account? Is it necessary that suspense account will balance off after rectification of the errors detected by the accountant? If not, then what happens to the balance still remaining in suspense account?
Solution:
In certain cases, when the debit column and the credit column of a trial balance do not agree, then the difference of the trial balance is transferred to a temporary account which is called a suspense account. This account is created to avoid any delay in creation of the financial statements. If the debit column falls short of the credit column, then the suspense account is debited and if the credit column falls short of the debit column then the suspense account is credited.

When all the errors are detected and rectified, then the suspense account automatically gets balanced. However, when errors still exist and are not rectified, the suspense account will not balance off and the balance amount of the suspense account will have to be transferred to the balance sheet. The debit balance of the suspense account is shown on the assets side and the credit balance is shown on the liabilities side of the balance sheet.

Q7. What kinds of errors would cause difference in the trial balance? Also list examples that would not be revealed by a trial balance? 
Solution:
One-sided errors are the errors which when committed affect the agreement of the trial balance. These errors affect only one account and any one side i.e. debit or the credit side of the account. Errors of partial omission, recording transactions with wrong amount, casting, posting of incorrect amount are examples of one-sided errors.
Two-sided errors do not affect the agreement of the trial balance. Here, are a few examples which would not be revealed in a trial balance:

1. Purchases from Mr. Shah, completely omitted to be recorded in the purchase book.
2. Purchases made from Vijesh, recorded in Ritesh’s account who is another creditor.
3. Stationary purchased for office use recorded in the purchase book.

Long Answer Type Questions

Q1. Describe the purpose for the preparation of trial balance. 

ANSWER: The important purposes for which the trial balance was prepared are explained with the help of the following points:

1. Ascertain the arithmetical accuracy of ledger accounts – The trial balance helps to ascertain whether all the debits and credits are properly recorded in the ledger. When the debit and the credit balances are equal, it is said that the posting and the balancing of the accounts is arithmetically correct. However, the tallying of the trial balance cannot be considered as a conclusive proof of accuracy of the books.
2. Helps in locating errors – When a trial balance does not tally, it helps in detecting or locating the errors. The error may have occurred at any one of the stages of an accounting process; namely,
   1. Totaling of the subsidiary books
   2. Posting of journal entries in the ledger
   3. Calculating account balances
   4. Carrying account balances to the trial balance
   5. Totaling the trial balance columns
3. Helps in the preparation of the financial statements – Trial balance is a statement which lists the debit and credit balances of all ledger accounts and helps in the preparation of the financial statements. Hence, it is considered as a connecting link between the accounting records and the preparation of financial statements.

Q2. Explain errors of principle and give two examples with measures to rectify them.

ANSWER: Generally accepted accounting principles are to be followed to record the accounting entries. When accounting entries are recorded violating or ignoring these principles, the error, thus, committed is known as error of principle. These errors do not affect the agreement of the trial balance.

Wages paid for construction of building are debited to wages account.
Wrong entry:

Wages A/c	Dr.
	To Cash A/c
(Being wages paid for construction of building)

Wages paid for the construction of building is to be treated as a capital expenditure and has to be debited to the building account instead of the wages account. Thus, the correct entry is

Building A/c	Dr.
	To Cash A/c
(Being wages paid for construction of building)

Hence, to rectify the error Building A/c needs to be debited and Wages A/c needs to be credited as it was wrongly debited. The rectifying entry is:

Building A/c	Dr.
	To Wages A/c
(Being wages paid for construction of building wrongly debited to wages account, now rectified)

Furniture purchased for Rs.10,000 wrongly debited to purchases account.
Wrong entry made:

Purchase A/c	Dr.
	To Cash A/c
(Being furniture purchased wrongly debited to purchases account)

Furniture is an asset and the purchase of the same should be debited to furniture account instead of purchases account. Thus, the correct entry is:

Furniture A/c	Dr.
	To Cash A/c
(Being old machinery sold for cash)

To rectify this error, Furniture A/c needs to be debited and Purchase A/c needs to be credited as it is wrongly debited. Thus, the rectifying entry is:

Furniture A/c	Dr.
	To Purchase A/c
(Being furniture purchased for wrongly debited to purchases account, now rectified)

Q3. Explain the errors of commission and give two examples with measures to rectify them.
ANSWER: The errors which are committed because of wrong posting of transactions, wrong balancing of accounts, wrong casting of subsidiary books, wrong totaling or wrong recording of amount in the books are all error of commission. These errors affect the agreement of the trial balance.

1. Purchases done from Rohan worth Rs.10,000 recorded as Rs.1,000.
Here, the transaction is recorded for Rs.1,000 instead of Rs.10,000. This is an error of wrong recording of amount. Purchases A/c requires a further debit of Rs.9,000 and Rohan’s A/c requires a further credit of Rs.9,000.The rectifying entry is:

Purchases A/c	Dr.	9,000
	To Rohan’s A/c			9,000
(Being goods purchased from Rohan of Rs.10,000 wrongly recorded as Rs.1,000, now rectified)

2. Sales book totaled as Rs.5,000 instead of Rs.50,000.
Here, the total sales of the book are short by Rs.45,000. This error can be rectified at any of the following two stages:

1. If the error is located before preparing trial balance, then Rs.45,000 should be recorded in the credit side of Sales Account.
2. If an error is located after preparing Trial Balance, then assuming that a suspense account is opened the following entry needs to be recorded.

Suspense A/c	Dr.		45,000
	To Sales A/c		45,000
(Being sales book wrongly totaled as Rs.5,000 instead of Rs.50,000)

Q4. What are the different types of errors that are usually committed in recording business transaction?
ANSWER:  According to the nature of errors committed, errors are classified into the following four categories:

1. Errors of Commission: The errors that are committed because of wrong posting of transactions, wrong balancing of accounts, wrong casting of subsidiary books, wrong totaling or wrong recording of amount in the books are all error of commission. These errors affect the agreement of the trial balance.
2. Errors of Omission: These errors are of two types and are committed when a transactions is partially or completely omitted to be recorded in the books.
   1. Error of complete omission – When a transaction is completely omitted to be recorded in the books of accounts or to be posted in the respective ledgers, it is an error of complete omission. Such errors do not affect the agreement of the trial balance.
   2. Error of partial omission – When a transaction is partially omitted while recording in the books or amounts or partially omitted from posting in the ledger, it is an error of partial omission. Such errors affect the agreement of the trial balance.
3. Errors of Principle: Accounting transactions are to be recorded following certain principles. If any of the principle of accounting entries are violated or ignored and the error occurring due to such violation is called error of principle.
4. Compensating errors: When two or more errors are committed in such a way that the net effect of these errors on the debits and credits of accounts is nil, such errors are called compensating errors.

Q5. As an accountant of a company, you are disappointed to learn that the totals in your new trial balance are not equal. After going through a careful analysis, you have discovered only one error. Specifically, the balance of the Office Equipment account has a debit balance of Rs.15,600 on the trial balance. However, you have figured out that a correctly recorded credit purchase of pen-drive for Rs.3,500 was posted from the journal to the ledger with a Rs.3,500 debit to Office Equipment and another Rs.3,500 debit to creditors accounts. Answer each of the following questions and present the amount of any misstatement:
(a) Is the balance of the office equipment account overstated, understated, or correctly stated in the trial balance?
(b) Is the balance of the creditors account overstated, understated, or correctly stated in the trial balance?
(c) Is the debit column total of the trial balance overstated, understated, or correctly stated?
(d) Is the credit column total of the trial balance overstated, understated, or correctly stated?
(e) If the debit column total of the trial balance is Rs.2,40,000 before correcting the error, what is the total of credit column.
ANSWER:
Pen-drive is wrongly debited to office equipment account, instead of stationery account and supplier account is debited instead of crediting. Because of these mistakes, the following errors are committed:
a. The balance of office equipment is overstated by Rs.3,500
b. The balance of creditors account is understated by Rs.7,000
c. The total of the debit column of the trial balance is correctly stated.
d. The total of the credit column of the trial balance is understated by Rs.7,000.
e. If the total of the debit column of the trial balance is Rs.2,40,000 before rectifying error, the total of the credit column of the trial balance is Rs.2,33,000 (i.e., Rs.2,40,000 – Rs.7,000).

Short Answer type Question:

Q.1 State the need for the preparation of bank reconciliation statement?

ANSWER: The need to prepare Bank Reconciliation Statement are given below.

1. It helps in finding out the errors and omissions committed in the Cash Book and the Pass Book.
2. It shows uncleared cheques, which have already been debited in the Cash Book but have not been yet recorded in the Pass Book.
3. It helps in checking embezzlement of money from the bank account.
4. It helps in measuring the accuracy of the transactions recorded in the Cash Book.
5. It facilitates in preparing revised Cash Book that reflects true bank balance.

Q.2 What is a bank overdraft?

ANSWER: Bank overdraft is a liability to an account holder. When the account holder withdraws excess amount over his/her available bank balance, he/she runs a negative bank balance. The negative bank balance is an obligation to the account holder and is called bank overdraft. In other words, bank overdraft is the excess of withdrawal over deposits.

Q.3 Briefly explain the statement ‘wrongly debited by the bank’ with the help of an example.

ANSWER: Amount wrongly debited by the bank implies a situation when the  bank wrongly debits a Pass Book. The following are the common mistakes that occur in the Pass Book when bank wrongly debits the Pass Book.

1. Mistake occurs when any two account holders’ names are identical. For example, a cheque of Rs 2,000 issued by Mr. Prem Singh was wrongly paid through Mr. Prem Kumar’s account.
2. Mistake occurs in case a person has more than one account in a bank. For example, a cheque of Rs 1,000 issued from his Current Account was wrongly paid through his Savings Account.
3. Sometimes amounts of cheques are wrongly recorded. For example, payment of Rs 2,000 through cheque was wrongly debited in the Pass Book as Rs 20,000.

Q.4 State the causes of difference occurred due to time lag.

ANSWER: The causes of difference that occur due to time lag are given below.

1. When issued cheques are not presented for payment in the period for which Bank Reconciliation Statement is being prepared, i.e., date of issue and the date of presenting the cheques are not same.

Cheques are credited in the Cash Book on the date that is mentioned on it, while in the Pass Book, cheques are debited when they are presented for the payment. Sometimes, the holder of a cheque does not present the cheque for payment on date ehich is mentioned on Cheque. The time gap between the date of issue and the date of presenting cheque for payment in the bank may lead to difference between the Cash Book and the Pass Book balances.

2. When deposited cheques are not cleared in the period for which the Bank Reconciliation Statement is being prepared.

Usually, date of deposit of cheque and date of clearance are not same as the clearance of cheque takes time. The difference between the Cash Book and the Pass Book balances arise when a cheque is deposited at the end of a period for which the Bank Reconciliation Statement is prepared and the cheque gets clearance in the subsequent period.

Q.5 Briefly explain the term favourable balance as per cash book

ANSWER: Favourable balance (Debit Balance), as per the Cash Book, is an asset to an account holder. It is also known as debit balance as per the Cash Book. Favourable balance is the excess of total of debit side over total of credit side of a bank column of a Cash Book. In other words, favourable balance means excess of deposits over withdrawals.

Q.6 Enumerate the steps to ascertain the correct cash book balance.

ANSWER: Generally, differences between the Cash Book and the Pass Book arise due to the reason that items have not been recorded in the Cash Book. In order to ascertain the correct Cash Book balance, we need to prepare Corrected (Adjusted) Cash Book. The below given steps are involved in the preparation of Corrected (Adjusted) Cash Book.

Step 1: Note down the bank balance as per the Cash Book.

Step 2: Rectify all the errors committed in the Cash Book.

Step 3: Enter those transactions in the debit of the Cash Book, which are only in the credit of the Pass Book.

Step 4: Enter those transactions in the credit of the Cash Book that are only in the debit of the Pass Book.

Step 5: The Cash Book is totalled and balancing figure is calculated. This balancing figure is use for preparing BRS.

Long Answer Type Questions

Q1. What is a bank reconciliation statement? Why is it prepared?
Solution:
Business organisations maintain the cash book for recording cash and bank transactions. It shows the balance of both the accounts at the end of an accounting period.
Similarly, the bank also maintains an account for each customer in its book. All deposits made by the customer are recorded on the credit side of the account and all withdrawals are recorded on the debit side of the account.
A copy of this is sent to the customer by the bank. This is called pass book or bank statement. This statement is used by the firm to tally its bank transactions as recorded by the bank with the cash book. The balance of the cash book must tally with that of the pass book.
But as both the books are maintained by two different parties, the bank balances as shown by the cash book and that shown by the pass book do not always match. The entries in both the books are, thus, compared and the items because of which the difference has occurred are determined and rectified. Thus, to reconcile the balances of the cash book and the pass book, a statement is prepared. This statement is called the bank reconciliation statement.
Specimen of Bank Reconciliation Statement:

Q2. Explain the reasons where the balance shown by the bank passbook does not agree with the balance as shown by the bank column of the cash book.
Solution:
The reason for the error in balance between the cash book and pass book can be stated as follows:
Timing difference on recording of the transactions
While comparing the balances of both the accounts, transactions found usually appear only in the cash book or only in the pass book. Such differences are caused by the time gap in recording the transactions in the books relating to either receipts or payments.

• Transactions which appear in the cash book but not in the pass book:
  1. Cheques issued but not presented for payment at the bank
     The firm/customer issues cheques to its suppliers and creditors, but not all these cheques are presented to the bank. The entry in the cash book is made immediately on issue of the cheque but the bank will not pass an entry until the cheque is presented for payment.
  2. Cheques paid or deposited but not collected and credited by the bank
     Entry is passed by the firm in the cash book when it receives cheques from its debtors which increase the balance as per the cash book. But the bank credits the firm’s account only when they receive the payment from the customer’s bank or in other words, once the cheque is collected by the bank.
• Transactions which appear in the pass book but not in the cash book:
  1. Direct bank charges, commission and interest debited by the bank
     Bank provides us various services for which it levies some charges which is directly debited from the firm’s account. The firm will know of these charges only after she/he verifies the entries with the bank statement.
     Example: Interest on overdraft, unpaid cheques and cheque collection charges
  2. Expenses directly paid by the bank on behalf of the customers
     Depending upon the standing instruction of the customer, the bank makes regular payment on behalf of the customer. The bank debits the customer’s account when the payment is made but the firm will pass the entry in his book only after he receives the bank statement. Thus, the balance as per the pass book will be less than the balance in the cash book.
     Example: Insurance premium, telephone bills and rent
  3. Amounts directly deposited in the customer’s account
     There are times when the firm’s debtors deposit money or make payments directly into the firm’s bank account. This results in an increase in the balance of the bank account. As no intimation is received by the firm, there will be no record of the same in the cash book.
  4. Incomes directly collected by the bank on behalf of customer but not recorded in cash book
     As per the agreement between the customer and the bank, the bank directly accepts payments such as dividends and rents and credits the same into the customer’s account. This increases the balance as per the pass book and causes a decrease in the balance in the pass book.
  5. Cheques deposited dishonoured or bills discounted dishonoured
     The bank sometimes allows the facility of discounting the bills of the customers. If such a bill is dishonoured on its date of maturity, the same is debited to customers account. As this information is not available to the firm, there will be no entry in the cash book. Similarly, when a cheque deposited by the firm in the bank is dishonoured, the same is debited to the customer’s account. As a result, there is a difference between the balances of the cash book and the pass book.

Errors in recording transactions by the firm or by the bank
Errors such as wrong recordings relating to cheques deposited/issued, wrong totaling or omission can be committed by the bank or the firm which can cause a difference between the cash book and the pass book balance.
Example: Wrong recording can be passed by the bank because of the similarity in names of its customers or some error caused by the clerk of the bank.

Cheques received by the firm are sent to the bank without passing an entry in the cash book or cheques received from the customers are omitted to be sent to the bank but an entry has been passed in the cash book.

Q3. Explain the process of preparing bank reconciliation statement with amended cash balance.
Solution:
The below given steps are involved in the preparation of adjusted cash book.
Step 1: The bank balance as per the cash book is noted.
Step 2: All the errors committed in the cash book to be recorded are rectified.
Step 3: Transaction present only on the credit side of the pass book needs to be recorded on the debit side of the cash book.
Step 4: Transaction present only on the debit side of the pass book needs to be recorded on the credit side of the cash book.
Step 5: Total the cash book and find the balancing figure. This balancing figure is used for preparing the bank reconciliation statement.
The proforma of the bank reconciliation statement through amended balance is given below:

Short Answer type question:

Q.1Briefly state how the cash book is both journal and a ledger?

ANSWER: Transactions are recorded directly from source documents in the Cash Book, so there is no need to record transactions in the Journal book. Further, on the basis of the cash transactions recorded in the Cash Book, cash and bank balances can be determined, and so there is no need to prepare cash account (which is a part of ledger) separately. Thus, the Cash Book serves the purpose of both Journal as well as ledger.

Q.2 What is the purpose of contra entry?

ANSWER: Contra entry represents deposits or withdrawals of cash from bank or vice versa. The purpose of contra entry is to indicate the transactions that effect both cash and bank balances. This entry does not affect the financial positions of a business. A contra entry is recorded in both sides of a two column Cash Book and is denoted by ‘C’ in the ledger folio column.

Q.3 What are special purpose books?

ANSWER: Business transactions are large in number and difficult to record; so, journal is sub-divided for quick, efficient and accurate recording of the business transactions. Special purpose books like, sales book and purchases book are maintained for those transactions that are routine and repetitive in nature. Recording through these books is economical and enables division of work among accountants.

Q.4 What is petty cash book? How it is prepared?

ANSWER: Petty Cash Book is used for recording payment of petty expenses, which are of smaller denominations like postage, stationery, conveyance, refreshment, etc. Person who maintains petty cash book is known as petty cashier and these small expenses are termed as petty expenses.

It is prepared by two methods:

1. Ordinary system: In this case, a fixed sum of money is paid to petty cashier for the payment of petty expenses and after spending the whole amount, the account is submitted by the petty cashier to the main cashier.
2. Imprest system: In this case, a fixed sum of the money is given to the petty cashier in the beginning of a period and at the end of the period the amount spent by him is reimbursed, so that he has a fixed amount in the beginning of every new period

Q.5 Explain the meaning of posting of journal entries

ANSWER: Posting is the process of transferring the business transactions from Journal to ledgers.

Every transaction is first recorded in the Journal and subsequently transferred to their respective accounts.

Q.6 Define the purpose of maintaining subsidiary journal.

ANSWER: The process of accounting starts from identification of financial and non-financial events. Financial events are first recorded in a Journal. A small business has lesser number of transactions and thereby it may be possible to record these transactions through Journal entry. However, on the contrary, as the business grows, there will be voluminous number of transactions and the firm may experience difficulty, thereby it becomes tedious to record through Journal entry. Thus, in order to save time and effort, it is recommended to sub-divide Journal. Sub-division of Journal provides scope for division of work. This leads to the improvement of efficiency and effectiveness and infuses higher degree of accountability to the accountants for the specific subsidiary Journal assigned to them. The purposes of maintaining subsidiary Journal are given below.

1. It saves time and efforts in recording.
2. It enables division of work, leading to an enhancement of efficiency and effectiveness, as particular accountant takes care of particular books.
3. It also makes each accountant more responsible and accountable for the books assigned to them.
4. It records routine and repetitive transactions at one place, which leads to easy accessibility of information and hassle-free communication.

Q.7 Write the difference between return inwards and return outwards.

ANSWER:

Basis of Difference	Return Inwards	Return Outwards
Meaning	Goods sold to the customers, are returned by them.	Goods purchased are returned to the suppliers.
Balance	It has debit balance.	It has credit balance.
Treatment	It is deducted from Sales in the Trading Account.	It is deducted from Purchases in the Trading Account.
Issued	Credit note is prepared by the seller.	Debit note is prepared by the buyer.
Reduction	It reduces the payment from the Debtors.	It reduces the payment made to the Creditors.
Term	It is also termed as Sales Returns.	It is also termed as Purchases Returns.

Q.8 What do you understand by ledger folio?

ANSWER: Ledger folio is a page number of an account in ledger that is written in the L.F. column of a journal format. In journal entry, ledger folio number is written corresponding to the name of the account in the L.F. column. It helps in easy locating of the account in the ledger book. It reduces the time in recording and rechecking.

Q.9 What is difference between trade discount and cash discount?

ANSWER:

Basis of Difference	Trade Discount	Cash Discount
Meaning	It is allowed when goods are purchase or sold.	It is allowed at the time of payment.
Recording in books	It is recorded in invoice/bill but not in the books.	It is recorded in the discount column of the Cash Book’s debit side, if allowed, and credit side, if received.
Purpose	It is allowed to increase sale.	It is allowed for earlier payment.
Deduction	It is deducted from the price-list of the goods.	It is not deducted from the price-list of the goods.

Q.10 Write the process of preparing ledger from a journal.

ANSWER: The process of preparing ledger from Journal can be explained with the help of an example. Let us suppose that machinery is purchased from Mr. X, so, the journal entry will be:

Machinery A/c	Dr.
	To Mr. X Account

In this example, Machinery Account is debited and Mr. X Account is credited. Let us understand the process of preparing ledger from the journal entry.

Account which is debited in the entry:

Step 1: Indentify the account in ledger that is debited, i.e., ‘Machinery Account’.

Step 2: Enter date in the debit side of the ‘Machinery Account’ in the ‘Date’ column.

Step 3: Enter the name of the account as ‘Mr. X Account’ (which is credited in the entry) in the ‘Particulars’ column in the debit side of the Machinery Account.

Step 4: Enter the page number of the journal, where the entry is recorded in the ‘J.F.’ (journal folio) column.

Step 5: Post the corresponding amount in the ‘Amount’ column, which is recorded against ‘Machinery Account’ in the journal entry.

Account which is credited in entry:

Step 1: Indentify the account in ledger that is credited, i.e., ‘Mr. X Account’.

Step 2: Enter date in the credit side of ‘Mr. X Account’ in the ‘Date’ column.

Step 3: Enter the name of the account as ‘Machinery Account’ (which is debited in the entry) in the ‘Particulars’ column in the credit side of the ‘Machinery Account’.

Step 4: Enter the page number of the journal where the entry is recorded in the ‘J.F.’ (journal folio) column.

Step 5: Post the corresponding amount in the ‘Amount’ column, which is recorded against ‘Mr. X Account’ in the journal entry.

Long Answer Type Questions

Q1. Explain the need for drawing up the special purpose books.
Answer : The needs for drawing up the special purpose book are given below.
1. Quick and efficient recording: It is a time consuming process to record all the transactions in a journal. If there are separate books, then recording of transactions can be done more efficiently and timely. So, the need of special purpose book arises.
2. Repetitive nature: In every business, some transactions are similar and repetitive in nature. It will be more convenient to record all similar transactions at one place. For example, all credit sales transactions are recorded in the Sales Book.
3. Economical: It is more economical as recording through the special purpose books saves time and also enhances the efficiency of accountants and clerks.
4. Easy posting: If similar transactions are recorded at one place, posting becomes easier.
5. Complete information at one place: All information related to purchases, sales, cash receipts, payments, etc. are easily and hassle-free available.

Q2. What is cash book? Explain the types of cash book.
Answer : Cash Book is a book of original entry. It records all transactions related to receipts and payments of cash and deposits in and withdrawals from a bank in a chronological order. In the debit side of the cash book, the cash receipts are recorded in the cash column while all deposits into bank account are recorded in the bank column. On the contrary, in the credit side of the cash book, all cash payments are recorded in the cash column, while all payments through cheques are recorded in the bank column. Usually, it is prepared on monthly basis. Cash book also serves the purpose of principle book (i.e. cash account and bank account).

1. Single Column Cash Book: A single column Cash Book contains one column of amount on both sides, i.e., one in the debit side and other in the credit side. In the single column Cash Book, only cash transactions are recorded. In the debit side of the Cash Book, all cash receipts are recorded, while in the credit side all cash payments are recorded.
2. Double Column Cash Book: A double column Cash Book contains two columns of amount, namely cash column and bank column on both sides. In the cash column of Cash Book, all cash receipts and payments are recorded, according to the rule of Real Accounts. All deposits either in cash or through cheques into the bank account of the business are debited in the bank column and all withdrawals of cash and payments through cheques are credited in the bank column.

3. Triple Column Cash Book: In a triple column Cash Book, there are three columns of amount namely, cash, bank and discount. Discount allowed and discount received are recorded in the discount column. While in the debit side, discount allowed is recorded along with the receipts, either in cash or through cheque; whereas, in the credit side, discount received is recorded, along with the payments made either in cash or by issuing cheques.
4. Petty Cash Book: This book is used for recording payment of petty expenses, which are of smaller denominations like, postage, stationery, conveyance, refreshment, etc. is known as Petty Cash Book.
Q3. What is contra entry? How can you deal this entry while preparing double column cash book?
Answer : The transaction that is entered in either sides of the double column or three column cash book, affecting both cash and the bank balances concomitantly is called contra entry. These entries result in increase in cash balances and decrease in bank balances or vice versa. In other words, a debit of bank account leads to a credit of cash account and a credit of bank account leads to a debit of cash account. For example, Rs 200 cash deposited into bank. This transaction increases the bank amount on one hand; whereas, on the other hand reduces the cash balance. In this entry, in the debit side of the cash book, ‘Cash’ will be recorded with a balance of Rs 200 in the bank column and in the credit side of the cash book, ‘Bank’ will be recorded with a balance of Rs 200 in the cash column. This entry is a contra entry as it affects both cash and bank balance together. The contra entries are denoted by ‘C’.
Some transactions that lead to contra entry are given below.
1. Opening a bank account
2. Depositing cash into bank
3. Withdrawal from bank
These transactions are recorded in a double column Cash Book as done below.

Q4. What is petty cash book? Write the advantages of petty cash book?
Answer :
Petty Cash Book is used for recording payments of small expenses, which are of smaller denominations such as postage, stationery, conveyance, refreshment, etc. Person who maintains Petty Cash Book is known as petty cashier and these small expenses are termed as petty expenses.
It is prepared by the below given two methods.
1. Ordinary system: Under this system, a certain sum of money is given to the petty cashier for the payment of petty expenses. After spending the whole amount, the accounts are submitted by the petty cashier to the main cashier.
2. Imprest system: Under this system, a fixed sum of money is given to the petty cashier in the beginning of a period to meet the petty expenses to be incurred in that period. At the end of the period, the amount spent by the petty cashier is reimbursed. So, the petty cashier has the same fixed amount of money in the beginning of the next period.

The Performa of Petty Cash Book is given below.

Advantages of Petty Cash Book:
Simple method: Recording of transactions in a petty cash book is easy. In an analytical Petty Cash Book, there exists separate heads for different petty expenses, which makes recording much easier. Recording in a Petty Cash Book does not require formal knowledge of accounting principles and techniques.
Time saving: Recording in Petty Cash Book saves time and efforts of the chief cashier.
Efficient control: At the end of a period,Petty Cash Book is audited by the main cashier, so frauds and errors are less probable.
Convenient handling: Recording in Petty Cash Book is convenient, as entries are to be recorded under separate heads, which makes posting easier and quicker.

Q5. Describe the advantages of sub-dividing the Journal.
Answer : The advantages of sub division of Journal are given below.
1. Division of work: The lack of sub-division of Journal may lead to chaos and confusions, if large numbers of transactions are to be recorded through Journal entry by more than one accountant. There will be more inflexibility and lack of accountability among the accountants. Sub-division of Journal into Subsidiary Books facilitates division of work. Sub-division enables different accountants to work on different books. This will not only avoid confusions but also enhance the sense of accountability among the accountants.
2. Time saving: The art of recording through subsidiary book is time efficient and more effective as compared to recording through Journal entries.
3. Prompt information: The transactions of similar nature are recorded in a particular Subsidiary Book. This acts as a ready source to access information quicker than through Journal entry.
4. Creates Accountability: Sub-division of Journal entrusts accountants with higher degree of responsibility and accountability for maintaining subsidiary book that are assigned to them.
5. Easy checking: In case discrepancies or errors arise, they can be easily located and rectified, as lesser number of transactions is recorded in a Subsidiary Book than in a Journal.
6. Specialisation: The accountability, responsibility and division of work together enhance the specialisation of each accountant. This is because, routine and repetitive tasks are performed by each accountant.

Q6. What do you understand by balancing of account?
Answer: Accounts are prepared on weekly, fortnightly, monthly, quarterly or on daily basis. At the end of each period they are balanced. The balancing of the accounts is done in the manner given below.
1. The totals of the debit and credit of an account is calculated, to ascertain which one of them is higher.
2. The higher figure among debit and credit side is written in the grand total cell on both sides of the account, i.e., in debit and in credit side.
3. The next step is to ascertain the difference between the debit total and the credit total. This difference is called ‘Closing Balance’ or ‘Balance carried down’, and is denoted by ‘Balance c/d’.
4. The ‘Balance c/d’ will be shown either in the debit or credit side, whichever totals up into lower amount.
5. If ‘Balance c/d’ is written in the debit side, then the balance is called ‘Credit balance’. On the other hand, if ‘Balance c/d’ is written in the credit side, then the balance is called ‘Debit Balance’.
6. On closing the account, ‘Balance c/d’ is brought forward to the subsequent period, and it is written as ‘Balance b/d’.
Usually, the closing balances of real and personal accounts are forwarded to the next period by this manner. For nominal accounts, Steps 1 to 3 remain same and they are closed by transferring the closing balances either to Trading Account or to Profit and Loss Account.

Short Answer Type Questions

Q1. State the three fundamental steps in the accounting process.
Answer : The fundamental steps in the accounting process are diagrammatically presented below.

Q3. Should a transaction be first recorded in a journal or ledger? Why?
Answer : A transaction should be recorded first in a journal because journal provides complete details of a transaction in one entry. Further, a journal forms the basis for posting the transactions into their respective accounts into ledger. Transactions are recorded in journal in chronological order, i.e. in the order of occurrence with the help of source documents. Journal is also known as ‘book of original entry’, because with the help of source document, transactions are originally recorded in books. The process of recording the transactions in journal and then in ledger is presented in the below given flow chart.

Q4. Are debits or credits listed first in journal entries? Are debits or credits indented?
Answer : As per the rule of double entry system, there are two columns of ‘Amount’ in the journal format namely ‘Debit Amount’ and ‘Credit Amount’. The way of recording in a journal is quite different from normal recording. Journal entry is recorded in journal format in which the ‘Debit Amount’ column is listed before the ‘Credit Amount’ column.
Credits are indented. Indentation is leaving a space before writing any word. Journal entry has its own jargon. While journalising, in the ‘Particulars’ column of journal format, debited account is written first and credited account is in the next line leaving some space, which is indentation.

Q5. Why are some accounting systems called double accounting systems?
Answer : Some accounting systems are called double accounting systems because under this system there are two aspects of every transaction, i.e., every transaction has dual effect. Every transaction affects two accounts simultaneously, that is represented by debiting one account and crediting the other account. It is based on the fact that if there is receiver, there should be a giver.

Q6. Give a specimen of an account.

Q7. Why are the rules of debit and credit same for both liability and capital?
Answer :
Every business acquires funds from internal as well as from external sources. According to the business entity concept, the amount borrowed from the external sources together with the internal sources like, capital invested by the proprietor, is termed as liability to the business. Business entity concept treats business and business owner separately. Capital of the owner is treated as liability to the business because the business has to repay the amount of capital to the owner, in case of closure of the business. As liability incurred is credited, in the same way, fresh capital introduced and net profit increases the owner’s capital, and so, capital is credited. On the other hand, if liability is paid, it reduces liability, and so, it is debited. Similarly, drawings from capital and net loss reduce the capital, and so, capital is debited. Thus the rules of debit and credit are same for both liability and capital.
Q8. What is the purpose of posting J.F numbers that are entered in the journal at the time entries are posted to the accounts?
Answer : J.F. number is the number that is entered in the ledger at the time of posting entries into their respective accounts. It helps in determining whether all transactions are properly posted in their accounts. It is recorded at the time of posting and not at the time of recording the transactions.
The purpose of entering J.F. number in the ledger is because of the below given benefits.
1. J.F. number helps in locating the entries of accounts in the journal book. In other words, J.F number helps to locate the position of the related journal entry and subsidiary book in the journal book.
2. J.F. number in accounts ensures that recording in the books of original entry has been posted or not.

Q9. What entry (debit or credit) would you make to: (a) increase revenue (b) decrease in expense, (c) record drawings (d) record the fresh capital introduced by the owner.
Answer :
1. Increase in revenue
Increase in revenue is credited as it increases the capital. Capital has credit balance and if capital increases, then it is credited.
2. Decrease in expense
Decrease in expense is credited as all expenses have debit balance. If expense decreases, then it is credited.
3. Record drawings
Capital has credit balance; if the capital increases, then it is credited. If capital decreases, then it is debited. Drawings are debited as they decrease the capital.
4. Record of fresh capital introduced by the owner- credit
Capital has credit balance, if capital increases, then it is credited. The introduction of fresh capital increases the balance of capital, and so, it is credited.

Q10. If a transaction has the effect of decreasing an asset, is the decrease recorded as a debit or as a credit? If the transaction has the effect of decreasing a liability, is the decrease recorded as a debit or as a credit?
Answer :If a transaction has a decreasing effect on an asset, then this decrease is recorded as credit. This is because, as all assets have debit balance and if assets decrease, then it is credited. For example, sale of furniture results in decrease in furniture (asset); so, the sale of furniture will be credited.
If a transaction has a decreasing effect on a liability, then this decrease is recorded as debit. This is because all liabilities have credit balance. If the liability increases, then it is credited and if the liability decreases, then it is debited. For example, payment to the creditors results in a decrease in the creditors (liability); so, the creditors account will be debited.

Numerical Questions

Q1. Prepare accounting equation on the basis of the following:
(a) Harsha started business with cash Rs 2,00,000
(b) Purchased goods from Naman for cash Rs 40,000
(c) Sold goods to Bhanu costing Rs 10,000/- Rs 12,000
(d) Bought furniture on credit Rs 7,000

Q2. Prepare accounting equation from the following:

Answer:

Q3. Mohit has the following transactions, prepare accounting equation:

Answer:

Q4. Rohit has the following transactions:

Prepare the Accounting Equation to show the effect of the above transactions on the assets, liabilities and capital.
Answer:

Q5. Use accounting equation to show the effect of the following transactions of M/s Royal Traders:

Answer:

Q6. Show the accounting equation on the basis of the following transaction:

Answer:

Q7. Show the effect of the following transactions on Assets, Liabilities and Capital through accounting equation:

Answer :

Q8. Show the effect of the following transaction on the accounting equation:

Answer :

Q9. Transactions of M/s. Vipin Traders are given below.
Show the effects on Assets, Liabilities and Capital with the help of accounting Equation.

Answer:

Q10. Bobby opened a consulting firm and completed these transactions during November, 2005:
(a) Invested Rs 4,00,000 cash and office equipment with Rs 1,50,000 in a business called Bobbie Consulting.
(b) Purchased land and a small office building. The land was worth Rs 1,50,000 and the building worth Rs 3,50,000. The purchase price was paid with Rs 2,00,000 cash and a long term note payable for Rs 8,00,000.
(c) Purchased office supplies on credit for Rs 12,000.
(d) Bobbie transferred title of motor car to the business. The motor car was worth Rs 90,000.
(e) Purchased for Rs 30,000 additional office equipment on credit.
(f) Paid Rs 75,00 salary to the office manager.
(g) Provided services to a client and collected Rs 30,000
(h) Paid Rs 4,000 for the month’s utilities.
(i) Paid supplier created in transaction (c).
(j) Purchase new office equipment by paying Rs 93,000 cash and trading in old equipment with a recorded cost of Rs 7,000.
(k) Completed services of a client for Rs 26,000. This amount is to be paid within 30 days.
(l) Received Rs 19,000 payment from the client created in transaction (k).
(m) Bobby withdrew Rs 20,000 from the business.
Analyse the above stated transactions and open the following T-accounts:
Cash, client, office supplies, motor car, building, land, long term payables, capital, withdrawals, salary, expense and utilities expense.
Answer :
(a) The transaction (a) increases assets by Rs 5,50,000 (cash Rs 4,00,000 and office equipment Rs 1,5,000) it will be debited and on the other hand it will increase the capital by Rs 5,50,000, so it will be credited in capital account.

(b)
Purchase of land and small office building are assets. On one hand, the purchase of these items will increase their individual accounts and this will increase the total amount of the assets in the business; so, both the accounts will be debited. On the other hand, payment in cash on the purchase of these assets will decrease the cash balance, so cash account will be credited to the extent of amount paid. After payment for building in cash, the balance of building account will be transferred to creditors for building account. This will increase the amount of the creditors, which in turn will increase the total liabilities of the business. Long term payables are regarded as loan to the business that will increase both cash balance (due to intake of loan) as well as liabilities of the business.

Q11. Journalise the following transactions in the books of Himanshu:

Answer:

Q12. Enter the following Transactions in the Journal of Mudit :

Answer :

Q13. Journalise the following transactions:

Answer :

Q14. Jouranlise the following transactions in the books of Harpreet Bros.:
(a) Rs 1,000 due from Rohit are now bad debts.
(b) Goods worth Rs 2,000 were used by the proprietor.
(c) Charge depreciation @ 10% p.a for two month on machine costing Rs 30,000.
(d) Provide interest on capital of Rs 1,50,000 at 6% p.a. for 9 months.
(e) Rahul become insolvent, who owed is Rs 2,000 a final dividend of 60 paise in a rupee is received from his estate.
Answer :

Q15. Prepare Journal from the transactions given below :

Answer :

Q16. Journalise the following transactions, post to the ledger:

Answer :

Q17. Journalise the following transactions is the journal of M/s. Goel Brothers and post them to the ledger.

Answer :

Q18. Give journal entries of M/s. Mohit traders; post them to the Ledger from the following transactions:

Answer :

Q19. Journalise the following transaction in the Books of the M/s. Bhanu Traders and Post them into the Ledger.

Answer :

Q20. Journalise the following transaction in the Book of M/s. Beauti tradeRs Also post them in the ledger.

Answer:

Q21. Journalise the following transaction in the books of Sanjana and post them into the ledger:

Answer :

Long Answer type Question:

Q.1Describe the events recorded in accounting systems and the importance of source documents in those systems.

Irrespective whether a business is small or big, there would be n-amount of financial transactions which would take place. A human mind cannot grasp this much amount of information. So in such instances, the source documents come in handy. A source document always enables verifiability and acts as evidence in court. They ensure that transactions recorded in the books are free from personal biases.

Source document in accounting is important because of the below given reasons.

1. Systematic track of records
2. Detect and prevent frauds and errors
3. Alternative memory box
4. Verifying the transaction during the auditing process
5. Evidence in the count of law

Scenarios which are supported by source document are

1. Return of goods purchased on credit worth Rs. 500, supported by debit note
2. Deposits into bank worth Rs. 1000, supported by pay-in slips
3. Purchase of goods worth Rs. 1000 on credit, supported by purchase invoice/bill
4. Cash sales worth Rs. 2,000, supported by cash memo

The books of accounts only record events expressed in monetary terms and not the non-monetary events. For example, promotion of an employee is not recorded in the book but the salary increment is recorded at the time when salary is paid or due. Question LA 2

Describe how debits and credits are used to analyse transactions.Solution LA 2

An accounting system is of two types, single entry accounting system and double entry accounting system. Majority of the business use the double entry accounting system as it consists of dual aspect. Double entry system is a complete system of recording transaction in the books of accounts. Each transaction reveals two aspects, receiving aspect or incoming aspect or expenses/loss aspect known as debit aspect and giving aspect or outgoing aspect or income/gain aspect known as credit aspect. The dual aspect can be better understood by the help of an example; bought goods worth Rs.1000 on cash. This transaction affects two accounts with the same amount simultaneously. As goods are brought in exchange of cash, the cash balances in the business reduce by Rs.1000 i.e. the cash account is credited. Simultaneously, the amount of goods increases by Rs.1000, so purchase account will be debited.

Debit and credit depend on the nature of accounts involved; such as assets, expenses, income, liabilities and capital. There are five types of accounts.

1. Assets– This increases the profit earning capacity of the business over a long-term across various accounting periods. Examples of fixed assets are furniture, machinery, land, plant and buildings.For example, machinery purchased and payment is made by cheque. The journal entry isMachinery A/c  Dr.To Bank A/c Here, machinery and bank balance, both are assets to the firm. As machinery is purchased, so machinery account will increase, and will be debited. On the other hand, payment of machinery is being made by cheque that reduces the bank balance of the business, so bank account will be credited.
2. Expense– It is the costs incurred to maintain the profitability of business in the process of earning profits. This help in the generating revenues, business operations and production such as rent, wages, depreciation, interest, salaries. They are measured by the services rendered or the cost of assets during an accounting period. For example, rent paid. The journal entry is:Rent A/c Dr.To Cash A/cHere, rent is an expense. All expenses have debit balance. Hence, rent is debited. On the other hand, as rent is paid in cash that reduces the cash balances, so cash account is credited.
3. Liability– Liabilities refer to the financial obligations or debt which a business owes to others such as loans from banks, other persons or creditors for goods supplied. Long term liabilities are loans which are payable after a period of 1 year. Short term liabilities are obligations which are payable within a period of time.The journal entry is:Bank A/c  Dr.To Bank Loan A/cHere, loan from bank is a liability to the firm. As all liabilities have credit balance, so loan from bank has been credited because it increases the liabilities.
4. Income- It refers to the amount received from selling the products or providing services to customers, royalty and commission received; they are added to the capital.
   For example, rent received from tenant. The journal entry is:Cash A/c   Dr.To Rent A/cHere, rent is an income; hence, rent account has been credited and cash has been debited, as rent received increases the cash balances.
5. Capital- It refers to the amount invested in form of cash or asset by the owner in a firm’s business or organisation of his choice. It is a claim on the assets of the business and also it will be an obligation of the business towards the owner of the firm. On the balance sheet, the capital is shown on the liabilities side.For example, additional capital introduced by owner. The journal  entry is:Cash A/c  Dr.To Capital A/cThe amount of capital increases i.e. credited when additional capital is introduced. On the other hand, the cash account is debited when the cash balances decrease i.e. capital introduced in form of cash.

Q.2 Describe how accounts are used to record information about the effects of transactions.

In a business, recording each and every transaction is of utmost importance. Not doing so, can notably affect the financial status of the business.

A transaction is first recorded in the journal, the book of original entry. However, if the further details on expense, revenue, equity, liability or increase or decrease in assets are needed, an account is brought in use. A detailed record of the information relating to a financial transaction can be termed as an account. It helps in determining the financial position of the business.

There are some steps to record transactions in accounts; it can be easily understood with the help of an example.

Sold goods to Mr. X worth Rs. 40,000 on 12th April and received payment Rs. 40,000 on 25th April. The following journal entries will be recorded:

Date	Particulars	L.F	Debit Rs.	Credit Rs.
Apr. 12    Apr 25.	X’ A/c Dr To Sales(Goods sold on credit to Mr. X) Cash A/c Dr To X’s A/c(Cash received from Mr. X)	2218   1322	40,000    40,000	40,000    40,000

Step 1– Locate the account in ledger, i.e. Mr. X’s Account.

Step 2– Enter the date of transaction in the date column of the debit side of Mr. X’s Account.

Step 3– In the ‘Particulars’ column of the debit side of Mr. X’s Account, the name of corresponding account is to be written, i.e. ‘Sales’.

Step 4– Enter the page number of the ledger in the Journal Folio (J.F.) column of Mr. X’s Account.

Step 5- Enter the amount in the ‘Amount’ column.

Step 6- Same steps are to be followed to post entries in the credit side of Mr. X’s Account.

Step 7– After entering all the transactions for a particular period, balance the account by totaling both sides and write the difference in shorter side, as ‘Balance c/d’.

Step 8– Total of account is to be written on either sides.Question LA 4

What is a journal? Give a specimen of journal showing at least five entries.Solution LA 4

Journal is known to be the book of original entry. Any financial transaction which takes place is recorded first in a journal so that they can be used for future references. The recording is done as and when a transaction occurs i.e. in a chronological order.

Performa of Journal

In the books of…..

Date	Particulars	L.F.	DebitRs.	CreditRs.

Date– Date of the transaction is entered in the first column. This date is entered only once unless and until there is a change in the date of transaction. It should be entered in proper sequence.

Particulars- Details of business transactions like, name of the parties involved and the name of related accounts, are recorded.

L.F. – Page number of ledger account when entry is posted.

Debit Amount– Amount of debit account is written.

Credit Amount- Amount of credit account is written.

 Example:

Date	Transactions by Mr. Ram
April 01	Started business with cash Rs.1,13,000
April 06	Open a bank account Rs.40,000
April 12	Purchase goods for cash Rs.5,000
April 19	Goods sold for cash Rs.4,500
April 25	Goods sold to Mr. X Rs.3,400

Journal in the books of Mr. Ram 

Date	Particulars		L.F.	Dr. (Rs.)	Cr.(Rs.)
2014
Apr. 01	Cash A/c	Dr.		1,13,000
	To Capital A/c				1,13,000
	(Being business started with cash)
Apr.02	Bank A/c	Dr.		40,000
	To Cash A/c				40,000
	(Being bank account opened with cash)
Apr.12	Purchases A/c	Dr.		5,000
	To Cash A/c				5,000
	(Being goods purchased for cash)
Apr.19	Cash A/c	Dr.		4,500
	To Sales A/c				4,500
	(Being goods sold for cash)
Apr.25	Mr. X’s A/c	Dr.		3,400
	To Sales A/c				3,400
	(Being goods sold to Mr. X on credit)
	Total		1,62,900	1,62,900

Q.3Differentiate between source documents and vouchers.Solution

Basis of Difference	Source Documents	Vouchers
Meaning	It refers to the documents in writing, containing the details of events or transactions	When source document is considered as evidence of an event or transaction, then it is called voucher
Purpose	It is used for preparing accounting vouchers	It is used for analysing the transactions
Recording	It acts as a basis for preparing accounting voucher which helps in recording	It acts as a basis for recording transactions
Legality/Validity	It can be used as evidence in the court of law	It can be used for authenticating transactions
Prepared By	It is prepared by the those directly involved in the transactions or who are authorised to prepare or approve these documents	It is prepared by the authorised persons or by the accountants
Examples	Cash memo, invoice, and pay-in-slip	Cash memo, invoice, pay-in-slip (if used as evidence), debit note, credit note, cash vouchers, transfer vouchers

Q.4Accounting equation remains intact under all circumstances. Justify the statement with the help of an example.

Majority of the business prefers the double entry accounting system i.e. the dual aspect concept over single entry system as it consists of dual effect i.e. two kinds of amount, debit and credit which affects each transaction. It is based on the fact that if there is receiver, there should be a giver. However, at any point of time, the assets of a business entity will always be equal to the total of its liabilities and capital i.e. total claims.

The equation between the assets and claims can be read as follows: 

or Liabilities = Asset – Capital

or Capital = Assets – Liabilities

The equation can also be represented as:

Assets – Liabilities = Capital

Assets – Capital = Liabilities

The above equation cannot be altered. For example, 

1. Business started with cash Rs.1,00,000

Cash A/c Dr 

 To Capital A/c

Assets	=	Liabilities	+	Capital
Cash(1,00,000)				1,00,000

Assets decrease, as cash is invested into the business and capital increases. Thus the equality between LHS and RHS remains intact.

2. Goods purchased on credit Rs.20, 000

Assets	=	Liabilities	+	Capital
Cash 1,00,000	Stock 20,000	=	Creditors 20,000	+	1,00,000

Assets increase as well as liability increases, without disturbing the equality.

3. Goods purchased with cash Rs.25,000

Assets	=	Liabilities	+	Capital
Cash1,00,000(25,000)	Stock20,00025,000	=	20,000	+	1,00,000

As goods are purchased for cash, so cash balance reduces by Rs.25,000, but on the other hand, stock balance increases by Rs.25,000. Thus the total balance of LHS remains equal to the total claims. Question LA 7

Explain the double entry mechanism with an illustrative example.Solution LA 7

Majority of the business prefers the double entry accounting system i.e. the dual aspect concept over single entry system as it consists of dual effect i.e. two kinds of amount, debit and credit which affects each transaction. It is based on the fact that if there is receiver, there should be a giver.

If a business firm acquires an asset for cash, it has to give some other asset say cash or the obligation to pay for it in future. Thus, giver necessarily implies a receiver and a receiver necessarily implies a giver.

In double entry system, accounts are classified as shown below:

1. Personal Accounts: Accounting transactions relating to persons such as individuals, firms, bank and companies are known as personal accounts, such as Mr. A, M/s ABC and Co. etc.
   Rule of double entry system for personal accounts: Debit the receiver and credit the giver.For example: Cash paid to Mr. A.Mr. A’s A/cDr.To Cash A/c (Being cash paid to Mr. A)  
2. Impersonal Accounts: It relates to non living things. Impersonal accounts are further classified as real accounts and nominal accounts.
   1. Real Account– Accounting transactions relating to tangible assets such as properties, goods and cash and intangible assets such as patents and trademark are known as real accounts.Rule of double entry system for real accounts: Debit what comes in and credit what goes out.For example: Furniture purchased for cash.Furniture  A/cDr.To Cash A/c (Being furniture purchased for cash)  
   2. Nominal Account: Accounting transactions relating to incomes and expenses and gains and losses of the firm are known as nominal accounts.Rule of double entry system for nominal accounts:Debit all expenses and losses and credit all incomes and gains.
      For example : Rent paidRent A/cDr.To Cash A/c (Being rent paid)  
   
    

Q.5 What is a journal? Give a specimen of journal showing at least five entries.

Journal is known to be the book of original entry. Any financial transaction which takes place is recorded first in a journal so that they can be used for future references. The recording is done as and when a transaction occurs i.e. in a chronological order.

Performa of Journal

In the books of…..

Date	Particulars	L.F.	DebitRs.	CreditRs.

Date– Date of the transaction is entered in the first column. This date is entered only once unless and until there is a change in the date of transaction. It should be entered in proper sequence.

Particulars- Details of business transactions like, name of the parties involved and the name of related accounts, are recorded.

L.F. – Page number of ledger account when entry is posted.

Debit Amount– Amount of debit account is written.

Credit Amount- Amount of credit account is written.

 Example:

Date	Transactions by Mr. Ram
April 01	Started business with cash Rs.1,13,000
April 06	Open a bank account Rs.40,000
April 12	Purchase goods for cash Rs.5,000
April 19	Goods sold for cash Rs.4,500
April 25	Goods sold to Mr. X Rs.3,400

Journal in the books of Mr. Ram 

Date	Particulars		L.F.	Dr. (Rs.)	Cr.(Rs.)
2014
Apr. 01	Cash A/c	Dr.		1,13,000
	To Capital A/c				1,13,000
	(Being business started with cash)
Apr.02	Bank A/c	Dr.		40,000
	To Cash A/c				40,000
	(Being bank account opened with cash)
Apr.12	Purchases A/c	Dr.		5,000
	To Cash A/c				5,000
	(Being goods purchased for cash)
Apr.19	Cash A/c	Dr.		4,500
	To Sales A/c				4,500
	(Being goods sold for cash)
Apr.25	Mr. X’s A/c	Dr.		3,400
	To Sales A/c				3,400
	(Being goods sold to Mr. X on credit)
	Total		1,62,900	1,62,900

Distance Formula
The distance between two points A(x₁, y₁) and B (x₂, y₂) is given by

The distance of a point A(x, y) from the origin 0 (0, 0) is given by …….

Section Formula
The coordinates of the point which divides the joint of (x₁, y₁) and (x₂, y₂) in the ratio m : n internally, is

Mid-point of the joint of (x₁, y₁) and (x₂, y₂) is

X-axis divides the line segment joining (x₁, y₁) and (x₂, y₂) in the ratio -y₁ : y₂.

Y-axis divides the line segment joining (x₁, y₁) and (x₂, y₂) in the ratio -x₁ : x₂.

The coordinates of the centroid of the triangle whose vertices are (x₁, y₁), (x₂, y₂) and (x₃, y₃) is

Area of Triangle
The area of the triangle, the coordinates of whose vertices are (x₁, y₁), (x₂, y₂)and (x₃, y₃) is the absolute value of

If the points (x₁, y₁), (x₂, y₂) and (x₃, y₃) are collinear, then x₁ (y₂ – y₃) + x₂ (y₃ – y₁) + x₃ (y₁ – y₂) = 0.

Shifting of Origin
Let the origin is shifted to a point O'(h, k). If P(x, y) are coordinates of a point referred to old axes and P'(X, Y) are the coordinates of the same points referred to new axes, then x = X + h, y = Y + k.

Straight Line
Any curve is said to be a straight line if two points are taken on the curve such that every point on the line segment joining any two points on it lies on the curve. General equation of a line is ax + by + c = 0.

Slope or Gradient of Line
The inclination of angle θ to a line with a positive direction of X-axis in the anti-clockwise direction, the tangent of angle θ is said to be slope or gradient of the line and is denoted by m.
i.e. m = tan θ
The slope of a line passing through points P(x₁, y₁) and Q(x₂, y₂) is given by

Note: Slope of a line parallel to X-axis is zero and slope of a line parallel to Y-axis is not defined.

Angle between Two Lines
The angle θ between two lines having slope m₁ and m₂ is

• If two lines are parallel, their slopes are equal i.e. m₁ = m₂.
• If two lines are perpendicular to each other, then their product of slopes is -1 i.e. m₁m₂ = -1.

Various Forms of the Equation of a Line
If a line is at a distance k and parallel to X-axis, then the equation of the line is y = ± k.

If a line is parallel to Y-axis at a distance c from Y-axis, then its equation is x = ± c.

Slope-intercept form: The equation of line with slope m and making an intercept c on the y-axis, is y = mx + c.

One point-slope form: The equation of a line which passes through the point (x₁, y₁) and has the slope of m is given by y – y₁ = m (x – x₁).

Two points form: The equation of a line passing through the points (x₁, y₁) and (x₂, y₂) is given by

The Intercept form: The equation of a line which cuts off intercepts a and b respectively on the x and y-axes is given by xa+yb=1

The normal form: The equation of a straight line upon which the length of the perpendicular from the origin is p and angle made by this perpendicular to the x-axis is α, is given by x cos α + y sin α = p.

General Equation of a Line
Any equation of the form Ax + By + C = 0, where A and B are simultaneously not zero is called the general equation of a line.

Different Forms of Ax + By + C = 0
Slope intercept form: If B ≠ 0, then Ax + By + C = 0 can be written as

If B = 0, then x = – C / A which is a vertical line, whose slope is not defined and x-intercept is – C/A.

Intercept form If C ≠ 0, then Ax + By + C = 0 can be written as

where a = – C / A and b = – C/B
If C = 0, then Ax + By + C = 0 can be written as Ax + By = 0 which is a line passing through origin and therefore has zero intercept on the axes.

Normal form: The normal form of equation Ax + By + C = 0 is x cos α + y sin α = p where

Note: Proper choice of signs to be made so that p should be always positive.

Position of Points is Relative to a Given Line
Let the equation of the given line be ax + by + c = 0 and let the coordinates of the two given points be P(x₁, y₁) and Q(x₂, y₂).
The two points are on the same side of the straight line ax + by + c = 0, If ax₁ + by₁ + c and ax₂ + by₂ + c have the same sign.

The two points are on the opposite sides of the straight line ax + by + c = 0, If ax₁ + by₁ + c and ax₂ + by₂ + c have opposite sign.

Condition of concurrency for three given lines
a₁x + b₁y + c₁ = 0, a₂x + b₂y + c₂ = 0 and a₃x + b₃y+ c₃ = 0 is a₃(b₁c₂ – b₂c₁) + b₃(a₂c₁ – a₁c₂) + c₃(a₁b₂ – a₂b₁) = 0

Point of intersection of two lines
Let equation of lines be ax₁ + by₁ + c₁ = 0 and a₂x + b₂y + c₂ = 0, then their point of intersection is

Distance of a Point from a Line
The perpendicular distanced of a point P(x₁, y₁)from the line Ax + By + C = 0 is given by

Distance Between Two Parallel Lines
The distance d between two parallel lines y = mx + c₁ and y = mx + c₂ is given by

Sequence
A succession of numbers arranged in a definite order according to a given certain rule is called sequence. A sequence is either finite or infinite depending upon the number of terms in a sequence.

Series
If a₁, a₂, a₃,…… a_n is a sequence, then the expression a₁ + a₂ + a₃ + a₄ + … + a_n is called series.

Progression
A sequence whose terms follow certain patterns are more often called progression.

Arithmetic Progression (AP)
A sequence in which the difference of two consecutive terms is constant, is called Arithmetic progression (AP).

• An arithmetic progression (A.P .) is a sequence in which terms increase or decrease regularly by the same constant. This constant is called  common difference of the A.P. Usually, we denote the first term of A.P . by   a, the common difference by d and the last term by . The general term or the  n^th  term of the A.P. is given by 
• Single Arithmetic mean between any two given numbers a and b: A.M. = 
•  Arithmetic mean between two given numbers a and b:  form an A.P.
• If a constant is added to each term of an A.P., then the resulting sequence is also an A.P.
• If a constant is subtracted to each term of an A.P., then the resulting sequence is also an A.P.
• If each term of an A.P. is multiplied by a constant, then the resuting sequence is also an A.P.
• If each term of an A.P. is divided by a constant, then the resuting sequence is also an A.P.
• Sum of first  terms of an A.P.:  and , where  is the last term, i.e., .

GEOMETRIC PROGRESSION

• A sequence of non-zero numbers is said to be a geometric progression, if the ratio of each term, except the first one, by its preceding term is always the same. , where  is the first term and  is the common ratio.
•  term of a G.P.: 
• Sum of  terms of a G.P.:  if .
• Sum to infinity of a G.P.: 
• Geometric mean between a and b: 
•  Geometric means between a and b: 
• If all the terms of a G.P. be multiplied or divided by the same quantity the resulting sequence is also a G.P.
• The reciprocal of the terms of a given G.P. form a G.P.
• If each term of a G.P. be raised to the same power, the resulting sequence is also a G.P.

ARITHMETIC – GEOMETRIC SERIES

• A sequence of non-zero numbers is said to be a arithmetic-geometric series, if its terms are obtained on multiplying the terms of an A.P. by the corresponding terms of a G.P. For example:   
• The general form of an arithmetic-geometric series:
  
• n^th term of an arithmetic-geometric series:  of A.P. x  of G.P.
• Sum of n terms of some special series : 
• Sum of squares of first n natural numbers =
• Sum of cubes of fist n natural numebrs = 

Binomial Expression
An expression consisting of two terms, connected by + or – sign is called binomial expression.

Binomial Theorem
If a and b are real numbers and n is a positive integer, then

The general term of (r + 1)^th term in the expression is given by
T_r+1 = ⁿC_r a^n-r b^r

Some Important

General and Middle Terms

• Binomial Theorem: The expansion of a binomial for any positive integral n is given by Binomial Theorem, which is
  
• The coefficients of the expansions are arranged in an array. This array is called Pascal’s triangle.
• The general term of an expansion 
• The general term of an expansion 
• The general term of 
• The general term of 
• In the expansion , if n is even, then the middle term is the  term. If n is odd, then the middle terms are and  terms.
•  term from the end in  term fromt he beginning.
• Method to prove Binomial Theorem:

(a) Principle of Mathematical Induction.

(b) Combinatorial Method.

• Factorial notation:
  (i)  
  (ii) 
  (iii) 
  (iv) 

1. Fundamental Principle of Counting
2. Permutations
3. Combinations

Fundamental Principle of Counting

• Addition Law: If there are two operations such that such that they can be performed independently in  and  ways respectively, then either of the two operations can be performed in  ways.
• Multiplication: If one operation can be performed in  ways and if corresponding to each of the  ways of performing this operation, there are  ways of performing a second operation, then the number of ways of performing two operations together in .
• Factorial Notation: The continued product of first  natural numbers is called the ‘ factorial’ and is denoted by .
• 

Addition Principle: If an operation A can be performed in m ways and another operation S, which is independent of A, can be performed in n ways, then A and B can performed in (m + n) ways. This can be extended to any finite number of exclusive events

Factorial
The continued product of first n natural number is called factorial ‘n’.
It is denoted by n! or n! = n(n – 1)(n – 2)… 3 × 2 × 1 and 0! = 1! = 1

Permutation
Each of the different arrangement which can be made by taking some or all of a number of objects is called permutation.

Permutation of n different objects
The number of arranging of n objects taking all at a time, denoted by ⁿP_n, is given by ⁿP_n = n!
The number of an arrangement of n objects taken r at a time, where 0 < r ≤ n, denoted by nP_r is given by
ⁿP_r = n!(n−r)!

Properties of Permutation

Important Results on Permutation
The number of permutation of n things taken r at a time, when repetition of object is allowed is nr.

The number of permutation of n objects of which p1 are of one kind, p2 are of second kind,… pk are of kth kind such that p₁ + p₂ + p₃ + … + p_k = n is n!p1!p2!p3!…..pk!

Number of permutation of n different objects taken r at a time,
When a particular object is to be included in each arrangement is r. ^n-1P_r-1

When a particular object is always excluded, then number of arrangements = ^n-1P_r.

Number of permutations of n different objects taken all at a time when m specified objects always come together is m! (n – m + 1)!.

Number of permutation of n different objects taken all at a time when m specified objects never come together is n! – m! (n – m + 1)!.

Combinations
Each of the different selections made by taking some or all of a number of objects irrespective of their arrangements is called combinations. The number of selection of r objects from; the given n objects is denoted by ⁿC_r, and is given by
ⁿC_r = n!r!(n−r)!

Inequation
A statement involving variables and the sign of inequality viz. >, <, ≥ or ≤ is called an inequation or an inequality.

Numerical Inequalities
Inequalities which do not contain any variable is called numerical inequalities, e.g. 3 < 7, 2 ≥ -1, etc. Literal Inequalities Inequalities which contains variables are called literal inequalities e.g. x – y > 0, x > 5, etc.

Linear Inequation of One Variable
Let a be non-zero real number and x be a variable. Then, inequalities of the form ax + b > 0, ax + b < 0, ax + b ≥ 0 and ax + b ≤ 0 are known as linear inequalities in one variable.

Linear Inequation of Two Variables
Let a, b be non-zero real numbers and x, y be variables. Then, inequation of the form ax + by < c, ax + by > c, ax + by ≤ c and ax + by ≥ c are known as linear inequalities in two variables x and y.

Solution of an Inequality
The value(s) of the variable(s) which makes the inequality a true statement is called its solutions. The set of all solutions of an inequality is called the solution set of the inequality.

• The values of x, which make an inequality a true statement, are called solutions of the inequality.
• To represent x <  a (or x >  a) on a number line, put a circle on the number and dark line to the left (or right) of the number a.
• To represent x ≤ a (or  x ≥ a) on a number line, put a dark circle on the number and dark the line to the left (or right) of the number x.
• If an inequality is having ≤ or ≥ symbol, then the points on the line are also included in the solutions of the inequality and the graph of the inequality lies left (below) or right (above) of the graph of the equality represented by dark line that satisfies an arbitrary point in that part.
• If an inequality is having < or > symbol, then the points on the line are not included in the solutions of the inequality and the graph of the inequality lies tothe left (below) or right (above) of the graph of the corresponding equality represented by dotted line that satisfies an arbitrary point in that part.

• To remove the denominator when the sign of the value of the denominator is unknown, may be +ve or -ve: We multiply by the square of the denominator. Square of the denominator is always positive. On multiplication of an inequation by a positive number the sign of inequality does not change.
• Solution of a system of Linear Inequality: The solution set of a system of linear inequality in one variable is defined as the intersection of the solution sets of the linear inequality of the system. For example: If we have two solution sets  and  then solution of the system is the intersection of  and  i.e., 
• Properties of absolute values:
  (i)  i.e., 
  (ii)  i.e., 
  (iii)  or  i.e., 
  (iv)  or  i.e., 
• Triangle Inequality: , 

Solving Linear Inequations in One Variable
Same number may be added (or subtracted) to both sides of an inequation without changing the sign of inequality.

Both sides of an inequation can be multiplied (or divided) by the same positive real number without changing the sign of inequality. However, the sign of inequality is reversed when both sides of an inequation are multiplied or divided by a negative number.

Representation of Solution of Linear Inequality in One Variable on a Number Line
To represent the solution of a linear inequality in one variable on a number line. We use the following algorithm.

If the inequality involves ‘>’ or ‘<‘ we draw an open circle (O) on the number line, which indicates that the number corresponding to the open circle is not included in the solution set.

If the inequality involves ‘≥’ or ‘≤’ we draw a dark circle (•) on the number line, which indicates the number corresponding to the dark circle is included in the solution set.

Graphical Representation of the Solution of Linear Inequality in One or Two Variables
To represent the solution of linear inequality in one or two variables graphically in a plane, we use the following algorithm.

If the inequality involves ‘<’ or ‘>’, we draw the graph of the line as dotted line to indicate that the points on the line are not included from the solution sets.

If the inequality involves ‘≥’ or ‘≤’, we draw the graph of the line as a dark line to indicate the points on the line is included from the solution sets.

Solution of a linear inequality in one variable can be represented on number line as well as in the plane but the solution of a linear inequality in two variables of the type ax + by > c, ax + by ≥ c,ax + by < c or ax + by ≤ c (a ≠ 0, b ≠ 0) can be represented in the plane only.

Two or more inequalities taken together comprise a system of inequalities and the solution of the system of inequalities are the solution common to all the inequalities comprising the system.