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:

Given,

The ratio of a man’s age to his father’s age is 4 : 5

Let the age of man and his father is 24a and 30a

The ratio of man's age to his son’s age is 6 : 1

$$=$$>  Age of his son = 4a

Four years ago the ratio of ages of the man and his son = 11 : 1

$$=$$>  $$\frac{24a-4}{4a-4}=\frac{11}{1}$$

$$=$$>  $$24a-4=44a-44$$

$$=$$>  $$20a=40$$

$$=$$>   a = 2

$$\therefore\ $$The ratio of the age of the grand father to that of the grandson 12 years from now = 30a+12 : 4a+12

= 30(2)+12 : 4(2)+12

= 60+12 : 8+12

= 72 : 20

= 18 : 5

Hence, the correct answer is Option B