A says to B "I am twice as old as you were when I was as old as you are." The sum of their ages is 63 years. Find the difference of their ages?

Let the present age of A is x and present age of B is y.
Therefore, x + y = 63 ....(i)
Difference of their ages is = (x - y) years.
When A was as old as B then, A's age was 'y; years and B's age was [y - (x - y)] = (2y - x) years.
Given that present age of A is twice the past age of B.
∴ x = 2(2y - x)
⇒ 3x = 4y .....(ii)
From (i) and (ii)
x = 36 and y = 27
So the difference in age of A and B is 36 - 27 = 9 years.