The ages of Misha and Kamal are in the ratio of 2 : 3 respectively. After 6 years the ratioof their ages will be 7 : 9. What is the difference in their present ages?

Correct option is A

Given:

The present ages of Misha and Kamal are in the ratio 2:3.

After 6 years, the ratio of their ages will be 7:9.

Solution:

Let the present ages of Misha and Kamal be 2x and 3x respectively

After 6 years, Misha's age will be 2x + 6 and Kamal's age will be 3x + 6

The equation representing the ratio of their ages after 6 years is:

$$\frac{2x + 6}{3x + 6} = \frac{7}{9}$$​​

9(2x + 6) = 7(3x + 6)

18x + 54 = 21x + 42

54 - 42 = 21x - 18x

12 = 3x

x = 4

The present ages of Misha and Kamal are 2x = 8 and 3x = 12, respectively.

The difference in their present ages = 12 - 8 = 4 years