Solution:
Given:
The ratio of a man's age to his father's age = 4 : 5
The ratio of his age to his son's age = 6 : 1
Four years ago age ratio of man to his father = 11 : 14
Four years ago age ratio of man to his son = 11 : 1
Calculation:
The ratio of a man's age to his father's age = 4 : 5
Four years ago age ratio of man to his father = 11 : 14
According to the question
(4x - 4)/(5x - 4) = 11/14
⇒ 14 (4x - 4) = 11 (5x - 4)
⇒ 56x - 56 = 55x - 44
⇒ 56x - 55x = 56 - 44
⇒ x = 12
Present age of man = 4 × 12 = 48 years
Present age of father = 5 × 12 = 60 years
The ratio of age of man to his son's age = 6y : y
6y = 48
⇒ y = 8
Present age of son = 8 years
12 years after, age of father will be = 60 + 12 = 72 years
12 years after, age of his son = 8 + 12 = 20 years
∴ 12 years after age ratio of man' father to that of his son = 72 : 20 = 18 : 5
