Question

If twice the son's age in years is added to the father's age, the sum is $70$. But if twice the father's age is added to the son's age, the sum is $95$. Find the ages of father and son.

Answer 1

Suppose father's age(in years) be x and that of son's be y. Then,
$x+2y=70$
and, $2x+y=95$

This system of equations may be written as
$x+2y-70=0$
$2x+y-95=0$

By cross-multiplication, we get

$\frac{x}{2\times -95-(-70)}=\frac{-y}{1\times -95-2\times -70}=\frac{1}{1\times 1-2\times 2}$

$\Rightarrow \frac{x}{-190+70}=\frac{-y}{-95+140}=\frac{1}{-3}$

$\Rightarrow \frac{x}{-120}=\frac{y}{-45}=\frac{1}{-3}$

$\Rightarrow x=\frac{-120}{-3}=40$ and $y=\frac{-45}{-3}=15$

Hence, father's age is $40$ years and the son's age is $15$ years.