#### Question

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

#### Solution

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 - x^{2} - 200 + 5x= 124

x^{2} - 45x + 324 = 0

x^{2} - 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

Is there an error in this question or solution?

Solution The Sum of the Ages of a Father and His Son is 45 Years. Five Years Ago, the Product of Their Ages (In Year) Was 124. Determine Their Presnet Ages. Concept: Solutions of Quadratic Equations by Factorization.