The ratio of the present ages of Rahim and Karim is 9 : 10 respectively. Twenty years ago, the ratio of their ages was 4 : 5 respectively. What is the present age of Rahim?

Question: The ratio of the present ages of Rahim and Karim is 9 : 10 respectively. Twenty years ago, the ratio of their ages was 4 : 5 respectively. What is the present age of Rahim?

Solution:
The ratio of the present ages of Rahim and Karim = 9 : 10
Let's consider the present ages of Rahim and Karim as 9x and 10x

According to the question,
(9x - 20) : (10x - 20) = 4 : 5
⇒ (9x - 20)/(10x - 20) = 4/5
⇒ 5(9x - 20) = 4(10x - 20)
⇒ 45x - 100 = 40x - 80
⇒ 45x - 40x = 100 - 80
⇒ 5x = 20
∴ x = 4

The present age of Rahim = (9 × 4) years.
= 36 years.