Question

Goodi is twice as old as Babli was when Goodi was as old as Babli is. The sum of their ages is 49. What is the difference between
their ages?

Answer 1

let, a=goodies
b= babli
When A was what B’s age is now, let X be the age of B, Y be the gap between the ages of A and B, and so A’s age was X + Y. 

They have now moved on Y years so that B is now what A was. 

Now B’s age is X + Y and A’s age is X + 2Y, but this also equals 2X by the statement “I am twice as old as you were when I was as old as you are” 

So, X + 2Y = 2X, giving X = 2Y 

Therefore A’s age was X + Y = 2Y + Y = 3Y and B’s age was X = 2Y 

Now A’s age is 3Y + Y = 4Y and B’s age is 2Y + Y = 3Y 

The present ages of A and B total 63, so 4Y + 3Y = 7Y = 49 which gives Y = 7 (the gap) 

Since X = 2Y = 14, we have the solution. 

A was 3Y = 21 and B was 2Y = 14 (7 years gap) 

A is now 4Y = 28 and B is now 3Y = 21 (7 years gap) 

A is now (28) twice what B was (14) when A was what B is now (21).