In a family, three sons were born for every 3 years one after the other. If the ratio of present ages of father and the eldest son is 15:7 and the average of the present ages of the 3 sons is 18 years. What will be the ratio of the ages of the father and the youngest son after 5 years?

Calculations:

Let the present age of the eldest son be '7x' (from the ratio of father and eldest son's age).

The present age of the father = 15x.

The sum of the present ages of the 3 sons = 3 × 18 = 54 years.

Since the sons were born 3 years apart, the second son’s age = (7x - 3) and the youngest son’s age = (7x - 6).

Sum of the ages of the 3 sons = 7x + (7x - 3) + (7x - 6) = 54

⇒ 7x + 7x - 3 + 7x - 6 = 54

⇒ 21x - 9 = 54

⇒ 21x = 63

⇒ x = 3

Now, the present age of the eldest son = 7x = 7 × 3 = 21 years.

The present age of the father = 15x = 15 × 3 = 45 years.

The present age of the youngest son = (7x - 6) = 21 - 6 = 15 years.

Father's age after 5 years = 45 + 5 = 50 years.

Youngest son's age after 5 years = 15 + 5 = 20 years.

The ratio of their ages after 5 years = 50 : 20 = 5 : 2.

∴ The ratio of the father's age to the youngest son's age after 5 years is 5 : 2.