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 age of father = x years
and
the present age of son = y years

According to question:

x + y = 45 ...(1)

Again, 5 years ago, the product of their ages was 124, therefore,

(Age of man 5 years ago) × (Age of son 5 years ago) = 124

(x – 5) × (y – 5) = 124

⇒ (45 – y - 5) ×(y – 5) = 124 [Using (1)]

⇒ \(40y – y^2 - 200 + 5y = 124 \)

⇒$y^2-45y+324=0$

⇒ $y^2-36y-9y+324=0$

⇒ $y(y-36)-9(y-36)=0$

⇒ (y - 36)(y - 9) = 0

⇒ y = 36 or y = 9

For y = 36, x = 45 - 36 = 9 which is not possible.

For y = 9, x = 45 - 9 = 36

Therefore, the present age of father = 36 years and the present age of son = 9 years.