The ratio between the present ages of A and B is 5 : 3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1 : 1. The ratio between A's age 4 years hence and B's age 4 year ago is:

Let the present ages of A and B are 5x and 3x years respectively. Then
A's age 4 years ago = 5x - 4
B's age 4 years hence = 3x + 4
According to question,
The ratio between A's age 4 years ago and B's age 4 years hence is 1 : 1
(5x - 4)/(3x + 4) = 1 : 1 = 1
⇒ 5x - 4 = 3x + 4
⇒ 2x = 8
∴ x = 4
present ages of A and B are 20 and 12 years.
The ratio between A's age 4 years hence and B's age 4 year ago is:
Hence, required ratio = (20 + 4) : (12 - 4) = 24 : 8 = 3: 1