CHAPTER -8 Comparing Quantities | CLASS 7TH |NCERT MATHS IMPORTANT QUESTIONS & MCQS | EDUGROWN

Answer: (a) 20 : 1
Hint:
Rs 10 : 50 paise = 10 × 100 paise: 50 paise
= 1000 : 50 = 20 : 1

Answer: (b) 15 : 1
Hint:
6 kg : 400 g = 6 × 1000 g : 400 g
= 6000 : 400 = 15 : 1.

Answer: (c) 5 : 1
Hint:
3 m : 60 cm = 3 × 100 cm : 60 cm
= 300 : 60 = 5 : 1.

Answer: (d) 5 : 1
Hint:
15 days : 72 hours
= 15 × 24 hours : 72 hours
= 15 × 24 : 72 = 5 : 1.

Answer: (c) 9 : 2
Hint:
45 years : 10 years ⇒ 9 : 2

Answer: (b) ₹ 25
Hint:
3 : 5 = 15 : x
⇒ 35 = 15x ⇒ x = 25

Answer: (d) 16 kg
Hint:
7. 7 : x = 42 : 96
⇒ 7x = 4296 ⇒ x = 16

Answer: (a) ₹ 90
Hint:
8. 4 : 9 = 40 : x
⇒ 49 = 40x ⇒ x = 90

Answer: (b) ₹ 25
Hint:
8 : 20 = 10 : x
⇒ 820 = 10x ⇒ x = 25

Answer: (c) 15 l
Hint:
120 : 600 = 3 : x
⇒ 120600 = 3x ⇒ x = 15

Answer: (b) 25%
Hint:
14 = 14 × 100% = 25%

Answer: (b) 121%
Hint:
18 = 18 × 100% = 1212%

Answer: (d) 250%
Hint:
52 = 52 × 100% = 250%

Answer: (b) 10%
Hint:
0.1 = 110 = 110 × 100% = 10%

Answer: (d) 4%
Hint:
0.04 = 4100 = 4100 × 100% = 4%

Answer: (c) 100%
Hint:
22 = 22 × 100% = 100%

Answer: (d) 25%
Hint:
Percentage of boys = 1040 × 100% = 25%

Important Questions

Question 1.
Find the ratio of:
(a) 5 km to 400 m
(b) 2 hours to 160 minutes
Solution:
(a) 5 km = 5 × 1000 = 5000 m
Ratio of 5 km to 400 m
= 5000 m : 400 m
= 25 : 2
Required ratio = 25 : 2
(b) 2 hours = 2 × 60 = 120 minutes
Ratio of 2 hours to 160 minutes
= 120 : 160
= 3 : 4
Required ratio = 3 : 4

Question 2.
State whether the following ratios are equivalent or not?
(a) 2 : 3 and 4 : 5
(b) 1 : 3 and 2 : 6
Solution:
(a) Given ratios = 2 : 3 and 4 : 5

Question 3.
Express the following ratios in simplest form:
(a) 615 : 213
(b) 42 : 56
Solution:

Question 4.
Compare the following ratios:
3 : 4, 5 : 6 and 3 : 8
Solution:
Given: 3 : 4, 5 : 6 and 3 : 8
or 34 , 56 and 38
LCM of 4, 6 and 8 = 24

Hence, 3 : 8 < 3 : 4 < 5 : 6

Question 5.
State whether the following ratios are proportional or not:
(i) 20 : 45 and 4 : 9
(ii) 9 : 27 and 33 : 11
Solution:
(i) 20 : 45 and 4 : 9
Product of extremes = 20 × 9 = 180
Product of means = 45 × 4 = 180
Here, the product of extremes = Product of means
Hence, the given ratios are in proportion.
(ii) 9 : 27 and 33 : 11
Product of extremes = 9 × 11 = 99
Product of means = 27 × 33 = 891
Here, the product of extremes ≠ Product of means
Hence, the given ratios are not in proportion.

Question 6.
24, 36, x are in continued proportion, find the value of x.
Solution:
Since, 24, 36, x are in continued proportion.
24 : 36 :: 36 : x
⇒ 24 × x = 36 × 36
⇒ x = 54
Hence, the value of x = 54.

Question 7.
Find the mean proportional between 9 and 16.
Solution:
Let x be the mean proportional between 9 and 16.
9 : x :: x : 16
⇒ x × x = 9 × 16
⇒ x² = 144
⇒ x = √144 = 12
Hence, the required mean proportional = 12.

Question 8.
Find:
(i) 36% of 400
(ii) 1623% of 32
Solution:

Question 9.
Find a number whose 614% is 12.
Solution:
Let the required number be x.

Hence, the required number = 192.

Question 10.
What per cent of 40 kg is 440 g?
Solution:
Let x% of 40 kg = 440 g

Hence, the required Percentage = 1.1%

Comparing Quantities Class 7 Extra Questions Short Answer Type

Question 11.
Convert each of the following into the decimal form:
(а) 25.2%
(b) 0.15%
(c) 25%
Solution:

Question 12.
What per cent of
(a) 64 is 148.48?
(b) 75 is 1225?
Solution:

Question 13.
A machine costs ₹ 7500. Its value decreases by 5% every year due to usage. What will be its price after one year?
Solution:
The cost price of the machine = ₹ 7500
Decrease in price = 5%
Decreased price after one year

= 75 × 95
= ₹ 7125
Hence, the required price = ₹ 7125.

Question 14.
What sum of money lent out at 12 per cent p.a. simple interest would produce ₹ 9000 as interest in 2 years?
Solution:
Here, Interest = ₹ 9000
Rate = 12% p.a.
Time = 2 years
Principal = ?

Hence, the required principal amount = ₹ 37500.

Question 15.
Rashmi obtains 480 marks out of 600. Rajan obtains 560 marks out of 700. Whose performance is better?
Solution:
Rashmi obtains 480 marks out of 600
Marks Percentage = 480600 × 100 = 80%
Rajan obtains 560 marks out of 700
Marks Percentage = 560700 × 100 = 80%
Since, both of them obtained the same per cent of marks i.e. 80%.
So, their performance cannot be compared.

Question 16.
₹ 9000 becomes ₹ 18000 at simple interest in 8 years. Find the rate per cent per annum.
Solution:
Here, Principal = ₹ 9000
Amount = ₹ 18000
Interest = Amount – Principal = ₹ 18000 – ₹ 9000 = ₹ 9000

Hence, the required rate of interest = 1212%.

Question 17.
The cost of an object is increased by 12%. If the current cost is ₹ 896, what was its original cost?
Solution:
Here, rate of increase in cost = 12%
Increased Cost = ₹ 896
Original Cost = ?
Let the Original Cost be ₹ x

Hence, the required cost = ₹ 800.

Comparing Quantities Class 7 Extra Questions Long Answer Type

Question 18.
Radhika borrowed ₹ 12000 from her friends. Out of which ₹ 4000 were borrowed at 18% and the remaining at 15% rate of interest per annum. What is the total interest after 3 years? (NCERT Exemplar)
Solution:
Total amount borrowed by Radhika = ₹ 12,000
The amount borrowed by her at 18% p.a. = ₹ 4000

Total interest = ₹ 2160 + ₹ 3600 = ₹ 5760
Hence, the total interest = ₹ 5760.

Question 19.
Bhavya earns ₹ 50,000 per month and spends 80% of it. Due to pay revision, her monthly income increases by 20% but due to price rise, she has to spend 20% more. Find her new savings. (NCERT Exemplar)
Solution:
Monthly income of Bhavya = ₹ 50,000
Money spent by her = 80% of ₹ 50,000
= 80100 × 50,000 = ₹ 40,000
Due to pay revision, income is increased by 20%

So, the new savings = ₹ 60,000 – ₹ 48,000 = ₹ 12,000

Question 20.
The simple interest on a certain sum at 5% per annum for 3 years and 4 years differ by ₹ 82. Find the sum.
Solution:
Let the required sum be ₹ P.
Simple interest for 3 years

Alternate Method
Simple Interest gained from 3rd to 4th year = ₹ 82
Time (4th year – 3rd year) = 1 year

Required sum = ₹ 1640

Comparing Quantities Class 7 Extra Questions Higher Order Thinking Skills (HOTS) Type

Question 21.
Rajan’s monthly income is 20% more than the monthly income of Sarita. What per cent of Sarita’s income is less than Rajan’s monthly income?
Solution:
Let the monthly income of Sarita be ₹ 100.
Rajan’s monthly income

Now, Sarita’s monthly income is less than the monthly income of Raj an by = ₹ 120 – ₹ 100 = ₹ 20
Per cent of less in Rajan’s monthly income
= 20×100120 = 503% = 1623%
Hence, the required per cent = 1623%

Question 22.
If 10 apples are bought for ₹ 11 and sold at the rate of 11 apples for ₹ 10. Find the overall gain or loss per cent in these transactions.
Solution:
CP of 10 apples = ₹ 11
CP of 1 apple = ₹ 1110
SP of 11 apples = ₹ 10
SP of 1 apple = ₹ 1011

Question 23.
If 25 men can do a work in 36 hours, find the number of men required to do the same work in 108 hours.
Solution:
Let the number of men required to be x.
Men : Hours :: Men : Hours
25 : 36 :: x : 108
Product of extremes = 25 × 108
Product of means = 36 × x
Product of means = Product of extremes
36 × x = 25 × 108
⇒ x = 25 × 3 = 75
Hence, the required number of men = 75.

Question 24.
A machine is sold by A to B at a profit of 10% and then B sold it to C at a profit of 20%. If C paid ₹ 1200 for the machine, what amount was paid by A to purchase the machine?
Solution:
Cost price of machine for C = Selling price of the machine for B = ₹ 1200

Hence, the required cost price = ₹ 9091011 or ₹ 909.09 (approx)