Given :-

Six years ago the ratio of ages of A&B was 1:3 and after six years the ratio becomes 2:3

To Find :-

Sum of present ages

Solution :-

Six years ago

A - 6/B - 6 = 1/3

3(A - 6) = 1(B - 6)

3A - 18 = B - 6

3A - B = 18 - 6

3A - B = 12 (1)

Now

A + 6/B + 6 = 2/3

3(A + 6) = 2(B + 6)

3A + 18 = 2B + 12

3A - 2B = 12 - 18

3A - 2B = -6

Subtract both

B = 18

Using 1

3a - 18 = 12

3a = 30

a = 30/3

a = 10

Sum = 18 + 10 = 28 years