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