let

a = the present age of Amit

s = the present age of Sumit

ages of Amit and Sumit are in ratio 2:3 means:

a : s = 2 : 3 cross-multiply

3a = 2s

after 15 years ratio will be 3:4

Amit's age after 15 years will be: a + 15

Sumit's age after 15 years will be: s + 15

(a + 15) : (s + 15) = 3 : 4 cross-multiply

4(a + 15) = 3(s + 15)

by solving the system of equations:

3a = 2s

4(a + 15) = 3(s + 15)

we find:

a = 30 years

s = 45 years

click here to see the step by step solution of the system of equations:

Amit's present age is 30 years.

Sumit's present age is 45 years.