The ratio of ages of 2 boys is 3 : 7. After 2 years, the ratio of their ages will become 5 : 9. The ratio of their ages after 10 years will be

13 : 17

The ratio of ages of 2 boys = 3 : 7.

After 2 years,

The ratio of their ages = 5 : 9

           3  :  7

           5  :  9

difference between 9 - 7 = 2 and 5 - 3 = 2

According to the question,

We can say, 2 = 2 years.

1 = 1 year

Then the age of first boy = 3 and the age of second boy = 7

After 10 years the ratio of their age = 3 + 10 : 7 + 10

= 13 : 17