Question

After five years, the age of son will be half the age of his father's present age. Five years ago, sum of their age was 75 years.

The present age of the father is years.

The present age of the son is years.

Solve using elimination method.

Answer 1

Let the present age of father and son is $x$ and $y$ years, respectively.

After $5$ years, age of son $=y+5$ years.
$\therefore y+5=\frac{x}{2}$
$\Rightarrow x-2y=10...\left(a\right)$

Five years ago, age of the father and son was $x-5$ and $y-5,$ respectively.
$\therefore (x-5)+(y-5)=75$
$\Rightarrow x+y=85...\left(b\right)$

Eliminating $y$ by subtracting $\left(a\right)$ from $\left(b\right)$ we get,
$x+y-(x-2y)=85-10$
$\Rightarrow y+2y=75$
$\Rightarrow y=\frac{75}{3}$
$\Rightarrow y=25$
Substituting in $\left(b\right)$ we get,
$\Rightarrow x=85-y$
$\Rightarrow x=85-25=60$

$\therefore$ Age of father and son is $60$ years and $25$ years, respectively.