RD SHARMA SOLUTION CHAPTER – 9 Ratio and Proportion | CLASS 7TH MATHEMATICS-EDUGROWN

Exercise 9.1

Question: 1

If x: y = 3: 5, find the ratio 3x + 4y: 8x + 5y.

Solution:

Question: 2

If x: y = 8: 9, find the ratio (7x – 4y): 3x + 2y.

Solution:

Question: 3

If two numbers are in the ratio 6:13 and their L.C.M is 312, find the numbers.

Solution:

Question: 4

Two numbers are in the ratio 3: 5. If 8 is added to each number, the ratio becomes 2: 3. Find the numbers

Solution:

Question: 5

What should be added to each term of the ratio 7: 13 so that the ratio becomes 2: 3

Solution:

Question: 6

Three numbers are in the ratio 2: 3: 5 and the sum of these numbers is 800. Find the numbers

Solution:

Question: 7

The ages of two persons are in the ratio 5: 7. Eighteen years ago their ages were in the ratio 8: 13. Find their present ages.

Solution:

Question: 8

Two numbers are in the ratio 7: 11. If 7 is added to each of the numbers, the ratio becomes 2: 3. Find the numbers.

Solution:

Question: 9

Two numbers are in the ratio 2: 7. 11 the sum of the numbers is 810. Find the numbers.

Solution:

Question: 10

Divide Rs 1350 between Ravish and Shikha in the ratio 2: 3.

Solution:

Question: 11

Divide Rs 2000 among P, Q, R in the ratio 2: 3: 5.

Solution:

Question: 12

The boys and the girls in a school are in the ratio 7:4. If total strength of the school be 550, find the number of boys and girls.

Solution:

Question: 13

The ratio of monthly income to the savings of a family is 7: 2. If the savings be of Rs. 500, find the income and expenditure.

Solution:

It is given that

The ratio of income and savings is 7: 2

Savings

2x = 500

So, x = 250

Therefore,

Income = 7 × 250 = 1750

Expenditure = Income – savings

= 1750 – 500

= Rs.1250

Question: 14

The sides of a triangle are in the ratio 1: 2: 3. If the perimeter is 36 cm, find its sides.

Solution:

Question: 15

A sum of Rs 5500 is to be divided between Raman and Amen in the rate 2: 3. How much will each get?

Solution:

Question: 16

The ratio of zinc and copper in an alloy is 7: 9. It the weight of the copper in the alloy is 11.7 kg, find the weight of the zinc in the alloy.

Solution:

Question: 17

In the ratio 7: 8. If the consequent is 40, what a the antecedent

Solution:

Given ratio = 7: 8

Consequent

8x = 40

x = 40/8

x = 5

antecedent = 7x = 7 × 5 = 35

Question: 18

Divide Rs 351 into two parts such that one may be to the other as 2: 7.

Solution:

Question: 19

Find the ratio of the price of pencil to that of ball pen, if pencil cost Rs.16 per score and ball pen cost Rs.8.40 per dozen.

Solution:

Question: 20

In a class, one out of every six students fails. If there are 42 students in the class, how many pass?

Solution:

Given,

One out of 6 student fails

x out of 42 students

16 = x/42

x = 42/6

x = 7

Number of students who fail = 7 students

No of students who pass =Total students – Number of students who fail = 42 – 7 = 35 students.

Exercise 9.2

Question: 1

Which ratio is larger in the following pairs?

(i) 3: 4 or 9: 16

(ii) 15: 16 or 24: 25

(iii) 4: 7 or 5: 8

(iv) 9: 20 or 8: 13

(v) 1: 2 or 13: 27

Solution:

Question: 2

Give the equivalent ratios of 6: 8.

Solution:

Question: 3

Fill in the following blanks:

Solution:

x = 3 and y =15

Exercise 9.3

Question: 1

Which of the following are in proportion?

(i) 33, 44, 66, 88

(ii) 46, 69, 69, 46

(iii) 72, 84, 186, 217

Solution:

Question: 2

Find x in the following proportions

(i) 16:18 = x: 96

(ii) x: 92 = 87: 116

Solution:

Question: 3

The ratio of income to the expenditure of a family is 7: 6. Find the savings if the income is Rs.1400.

Solution:

The ratio of income and expenditure = 7: 6

7x = 1400

x = 200

Expenditure = 6x = 6 × 200 = Rs.1200

Savings = Income – Expenditure

= 1400 -1200

= Rs.200

Question: 4

The scale of a map is 1: 4000000. What is the actual distance between the two towns if they are 5cm apart on the map?

Solution:

The scale of map = 1: 4000000

Let us assume the actual distance between towns is x cm

1: 4000000 =5: x

x = 5 × 4000000 = 20000000 cm

1km = 1000 m

1m = 100 cm

Therefore

x = 200 km

Question: 5

The ratio of income of a person to his savings is 10: 1. If his savings for one year is Rs.6000, what is his income per month?

Solution:

The ratio of income of a person to his savings is 10: 1

Savings per month = 6000/12

= Rs.500

Then let income per month be x

x: 500 = 10:1

x = 500 × 10

x = 5000

Question: 6

An electric pole casts a shadow of length 20 metres at a time when a tree 6 metres high casts a shadow of length 8 metres. Find the height of the pole

Solution:

Height of the tree: Length of the shadow of tree

Height of the pole: Length of the shadow of pole

x: 20 = 6: 8

x = 120/8

x = 15