In order to excel in the final examination, students can download the PDF of RD Sharma Solutions for Class 7 Maths Exercise 9.3 of Chapter 9 Ratio and Proportion. The PDF contains solutions for all questions present in the exercise solved by BYJU’S subject experts in Maths. By solving RD Sharma Solutions for Class 7, students will be able to solve all problems easily. This exercise explains the proportion and equality of two pairs. It also deals with continued proportion and mean proportion.
Download the PDF of RD Sharma Solutions for Class 7 Maths Chapter 9 – Ratio and Proportion Exercise 9.3
Access answers to Maths RD Sharma Solutions for Class 7 Chapter 9 – Ratio and Proportion Exercise 9.3
1. Find which of the following are in proportion?
(i) 33, 44, 66, 88
(ii) 46, 69, 69, 46
(iii) 72, 84, 186, 217
Solution:
(i) Given 33, 44, 66, 88
Product of extremes = 33 × 88 = 2904
Product of means = 44 × 66 = 2904
Therefore product of extremes = product of means
Hence given numbers are in proportion.
(ii) Given 46, 69, 69, 46
Product of extremes = 46 × 46 = 2116
Product of means = 69 × 69 = 4761
Therefore product of extremes is not equal to product of means
Hence given numbers are not in proportion.
(iii) Given 72, 84, 186, 217
Product of extremes = 72 × 217 = 15624
Product of means = 84 × 186 = 15624
Therefore product of extremes = product of means
Hence given numbers are in proportion.
2. Find x in the following proportions:
(i) 16: 18 = x: 96
(ii) x: 92 = 87: 116
Solution:
(i) Given 16: 18 = x: 96
In proportion we know that product of extremes = product of means
16/18 = x/96
On cross multiplying
x = (16 × 96)/ 18
x = 1536/18
Dividing both numerator and denominator by 6
x = 256/3
(ii) Given x: 92 = 87: 116
In proportion we know that product of extremes = product of means
x/ 92 = 87/116
On cross multiplying
x = (87 × 92)/ 116
x = 69
3. The ratio of income to the expenditure of a family is 7: 6. Find the savings if the income is Rs.1400.
Solution:
Given that income = 1400
Given the ratio of income and expenditure = 7: 6
7x = 1400
Therefore x = 200
Expenditure = 6x = 6 × 200 = Rs.1200
Savings = Income – Expenditure
= 1400 -1200
= Rs.200
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:
Given that the scale of map = 1: 4000000
Let us assume the actual distance between towns is x cm
1: 4000000 =5: x
x = 5 × 4000000
x = 20000000 cm
We know that 1km = 1000 m
1m = 100 cm
Therefore
x = 200 km
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:
Given that the ratio of income of a person to his savings is 10: 1
Savings per year = 6000
Savings per month =Â 6000/12
= Rs.500
Then let income per month be x
x: 500 = 10:1
x = 500 × 10
x = 5000
Income per month is Rs. 5000
6. An electric pole casts a shadow of length 20 meters at a time when a tree 6 meters high casts a shadow of length 8 meters. Find the height of the pole.
Solution:
Given that length electric pole shadow is 20m
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
Therefore height of the pole is 15 meters
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