Father’s present age is four times his son’s age. After 8 years, he will be two and a half times his son’s age. After another 8 years, what will be the ratio of the father’s age to the son’s age?

Question: Father’s present age is four times his son’s present age. After 8 years, the father’s age will be two and a half times his son’s age. After another 8 years, what will be the ratio of the father’s age to his son’s age?

Solution:
Let the son’s present age = x years
So, father’s present age = 4x years

After 8 years,
Son’s age = x + 8 years
Father’s age = 4x + 8 years

According to the question,
4x + 8 = (5/2)(x + 8)
⇒ 2(4x + 8) = 5(x + 8)
⇒ 8x + 16 = 5x + 40
⇒ 8x - 5x = 40 - 16
⇒ 3x = 24
⇒ x = 8

So,
Son’s present age = 8 years
Father’s present age = 4 × 8 = 32 years

After another 8 years means after total 16 years from present,
Son’s age = 8 + 16 = 24 years
Father’s age = 32 + 16 = 48 years

Therefore,
Father’s age : Son’s age = 48 : 24
= 2 : 1