Question

The sum of the ages of 3 persons is 150 years. 10 years ago their ages were in the ratio
7 : 8 : 9. Their present ages are

Answer 1

Answer :

• 45 , 50 and 55 respectively

Given :

1. Sum of ages of three persons is 150
2. Ratio 10 years back = 7:8:9

To Find :

• Present ages of three

Solution:

Let the ages of three persons be a , b and c years respectively .

A/Q

a + b + c = 150

10 years ago ,

a = a - 10

b = b -10

c = c -10

Before 10 years , sum of their ages

a + b + c = 150 - 30

a + b + c = 120

Let the common ratio be x .

A/Q

7x + 8x + 9x = 120

24x = 120

x = 120/24

x = 5

Ages 10 years before :

7 x = 7 × 5 = 35 years

8x = 8 × 5 = 40 years

9x = 9 × 5 = 45 years

Present ages :

$\implies$a = 35 + 10 = 45 years

$\implies$b = 40 + 10 = 50 years

$\implies$c = 45 + 10 = 55 years

$\underline{\therefore \tt {\orange{The\ present\ ages\ are\ 45\ , 50\ and\ 55}}}$

Verification :

a + b + c = 150

45 + 50 + 55 = 150

150 = 150