Question

The ages of P and Q are in the ratio 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7. Find their ages.

Answer 1

Let the common multiple be x.
So, P's age be 7x years and Q's age be 5x years.
10 years hence, means after 10 years.
As per the given condition,

`(7x + 10)/(5x + 10) = (9)/(7)`

⇒ 7(7x + 10) = 9(5x + 10)
⇒ 49x + 70 = 45x + 90
⇒ 49x - 45x = 90 - 70
⇒ 4x = 20
⇒ x = 5
P's age = 7 years = 7(5) = 35years
Q's age = 5x = 5(5) = 25 years
Hence, P's age is 35 years and Q's age is 25 years.