Question

The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present ages.

Answer 1

Let the present ages of father and his son be x years and (45 – x) years respectively.

Five years ago,

Father's age = (x – 5) years

Son's age = (45 – x – 5) years = (40 – x) years

From the given information, we have:

(x – 5)(40 – x) = 124

40x – x² – 200 + 5x = 124

x² – 45x + 324 = 0

x² – 36x – 9x + 324 = 0

x(x – 36) – 9(x – 36) = 0

(x – 36)(x – 9) = 0

x = 36, 9

if x = 9,

Father's age = 9 years,

Son's age = (45 – x) = 36 years

This is not possible.

Hence, x = 36

Father's age = 36 years

Son's age = (45 – 36) years = 9 years.