Page 98 - ICSE Math 7

72 x
2
⇒ x = ⇒ x × x = 72 × 8 ⇒ x = 72 × 8
8
2
⇒ x = 576 ⇒ x = 24 × 24 ⇒ x = 24
So, 24 is the mean proportional between 72 and 8.
Example 15: Find the third proportional to 12 and 24.
Solution: Let the third proportional be x.

∴ 12, 24 and x are in continued proportion.
12 24
⇒ = ⇒ 12 × x = 24 × 24
24 x
24 × 24
⇒ x = = 48
12
So, 48 is the third proportional to 12 and 24.

Example 16: If x : y = 3 : 2 and y : z = 5 : 4, find x : y : z.
3 2 3
Solution: x : y = 3 : 2 = : = : 1
2 2 2
Similarly, y : z = 5 : 4
4
5
= : = 1 : 4
5
5
5
3 4
Thus, x : y : z = : 1 :
2 5
 3   4 
×
=  2 × 10 : ( 110) :  5 × 10 (LCM of 2 and 5 = 10)






= 15 : 10 : 8
Example 17: Rohit has three bags. The first bag weighs 2 kg 500 g and the third bag weighs 10 kg.
Find the weight of the second bag if its weight is mean proportional between the weights
of the other two bags.
Solution: Let the weight of the second bag be x kg.
500 1 5
Weight of first bag = 2 kg 500 g = 2 1000 kg = 2 kg = kg
2
2
5
So, kg, x kg and 10 kg are in continued proportion.
2
5 1 x 5
2
⇒ × = ⇒ x = × 10 = 25
2 x 10 2
2
⇒ x = 5 × 5 ⇒ x = 5
∴ Weight of the second bag is 5 kg.

EXERCISE 7.2

1. Find x such that:
(a) x : 7 = 12 : 84 (b) 102 kg : x :: 34 m : 110 m (c) x : 12 :: 12 : 7
1 1
(d) 0.8 : 2.4 :: x : 7.5 (e) 28 g : 140 g :: 17 kg : x (f) 4 : 3 = x : 20
3
3
2. Find the fourth proportional to the following.
1 1 1 5 1 1 1
(a) 2, 5, 4 (b) 6, 4, (c) 1.4, 1.6, 3.5 (d) 2 , 1 , 1 (e) , ,
2 3 2 9 3 2 6

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