Question

The sum of 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 $x$ years be the present age of the father, then the present age of the son will be $\left(45-x\right)$ years.

Five years ago, the age of father was $\left(x-5\right)$ years and that of son was $\left(45-x-5\right)=\left(40-x\right)$ years.

As, five years ago, the product of ages was 124.

$\left(x-5\right)\left(40-x\right)=124$

$\Rightarrow x^2-45x+324=0$

$\Rightarrow \left(x-9\right)\left(x-36\right)=0$

$\Rightarrow x=9,x=36$

When $x=36$, the age of father is 36 and the age of son is 9 years.

When $x=36$, the age of the father is 9 years and the age of the son is 36 years, which cannot be possible, so the present age of father is 36 years and that of the son is 9 years.