Question

A father is $25$ years older than his son. After $8$ years the ratio of their ages will be $13:8$. Find their present ages

Answer 1

Let the age of son be $x$ years.

Thus, age of father is $x+25$ years.

After $8$ years, their ages will be

Age of son $x+8$ and age of father $x+25+8=x+33$.

The ratio of their ages is $13:8$.

Therefore, $\frac{x+33}{x+8}=\frac{13}{8}$

$\Rightarrow 8(x+33)=13(x+8)$

$\Rightarrow 8x+264=13x+104$

$\Rightarrow 13x-8x=264-104$

$\Rightarrow 5x=160$

$\Rightarrow x=32$

Age of son is $32$ years.

Thus, age of father is $x+25=32+25=57$ years.