Ratio & Proportion (Exercise 9.3) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

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Exercise 9.3 Page No: 9.13 
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, we get,
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Exercise 9.3 Page No: 9.13 
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, we get,
  
 
 
 
 
  
 
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 
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Exercise 9.3 Page No: 9.13 
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, we get,
  
 
 
 
 
  
 
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 = 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