The ratio between the present ages of A and B is 3 : 5. If the ratio of their ages five years hence becomes 13 : 20, then the present age of B is:

Question: The ratio between the present ages of A and B is 3 : 5. If the ratio of their ages five years hence becomes 13 : 20, then the present age of B is:

Solution:
Let's say A's present age is 3x and B's present age is 5x
After 5 years,
A's age will be = 3x + 5
B's age will be = 5x + 5

ATQ,
(3x + 5)/(5x + 5) = 13/20
⇒ 20(3x + 5) = 13(5x + 5)
⇒ 60x + 100 = 65x + 65
⇒ 60x - 65x = 65 - 100
⇒ - 5x = - 35
∴ x = 7

Since B's present age = 5x = 5 × 7 = 35 years