The ratio of a man’s age to his father’s age is 4 : 5, and the ratio of his age to his son’s age is 6 : 1. Four years ago these ratios were 11 : 14 and 11 : 1, respectively. The ratio of the age of the grand father to that of the grandson 12 years from now will be:

18 : 5

At present , Men's age : Father age = 4 : 5 ,  Men's age : Son's age = 6 : 1

Grandfather's age : Grandson's age = 15 : 2

4 years ago ,

Men's age : Father age = 11 : 14 ,  Men's age : Son's age = 11 : 1

Grandfather's age : Grandson's age = 14 : 1

ATQ,

\(\frac{14x + 4 }{x + 4}\) = \(\frac{15}{2}\)

28x + 8 = 15x + 60

13x = 52

x = 4

Age of grandfather after 12 years = 14 × 4 + 4 + 12 = 72

Age of grand son after 12 years = 4 × 1 + 4 + 12 = 20

Ratio of age of grandfather to grandson 12 years hence = 72 : 20

= 18 : 5