Present ages of X and Y are in the ratio 5 : 6 respectively. After seven years this ratio becomes 6 : 7. What is the present age (in years)…

Present age of X and Y are in ratio 5 : 6

So, let their ages be 5x and 6x respectively.

After 7 years their ages will be (5x + 7) and (6x + 7) respectively.

Now they are in ratio 6 : 7,

So let it be 6y and 7y respectively.

This means

5x + 7 = 6y ------(1)

6x + 7 = 7y ------(2)

Multiplying equation (1) by 7 and (2) by 6 and solving we get:

x = 7, then X = 5x = 5 × 7 = 35

Therefore present age of X is 35 years.