Question

Rakesh is $19$ years younger than his father. After $5$ years, their ages will be in the ratio $2:3$. Find their present ages.

Answer 1

Let age of Rakesh father be x

then age of Rakesh = x-19

after 5 years

age of Rakesh father = x+5

age of Rakesh father = x-19+5=x-14

then

$\Rightarrow \frac{x+5}{x-14}=\frac{3}{2}$

$\Rightarrow 3x-42=2x+10$

$\Rightarrow 3x-2x=52$

[x=52]

$\therefore$ age of Rakesh father is 52

then age of Rakesh is 33.