Correct Answer - Option 2 : 8 ∶ 11

The ratio between the present ages of M and N = 5 ∶ 8

Let present age of M = 5x

Present age of N = 8x

According to Question:

Age of N = Age of M + 6

8x = 5x + 6

3x = 6

x = 2

So, the present age of M = 5x = 5 × 2 = 10 years

The present age of N = 8x = 8 × 2 = 16 years

After 6 years:

Age of M = 10 + 6 = 16 years

Age of N = 16 + 6 = 22 years

The ratio of the ages of M and N after 6 years = 16 : 22

= 8 : 11

Hence, **"8 : 11" **is the correct answer.