Exercise 9.3
1. Which of the following are in proportion?
(i) 33, 44, 66, 88
Solution:
We have,
∴ 33 : 44 = 66: 88
Thus, 33: 44, 66, 88 are in pro proportion
(ii) 46, 69, 69, 46
Solution:
We have:
∴ 46: 69 ≠ 69: 46
Thus, 46, 69, 69, 46 are not in proportion.
(iii) 72, 84, 186, 217
Solution:
We have,
72, 84, 184, 217
Thus, 72, 84, 186, 217 are in proportion.
2. Find x in the following proportions
(i) 16:1= x:96
Solution:
(ii) x:92 = 87 : 116
Solution:
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
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
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
Than let income per month be x
X: 5000 = 10: 1
X = 500×10
X = 5000
Income per month is Rs. 5000
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
