Question

A father's age is $3$ times the sum of ages of his two children. After $5$ years his age will be twice the sum of ages of his two children. Find the age of the father.

Answer 1

Let the age of two children be x and y respectively.

$\therefore$ father's present age $=3(x+y)$

father's age after 5 years $=3(x+y)+5.....\left(1\right)$

Also given that, after 5 years his age will be twice the sum of ages of his two children.

$\therefore$ After 5 years, age of both children will be $(x+5)$ and $(y+5)$ respectively.

$\therefore$ father's age after 5 years $=2\times ((x+5)+(y+5))=2x+2y+20.....\left(2\right)$

From ${eq}^n\left(1\right)\&\left(2\right)$, we have

$2x+2y+20=3x+3y+5$

$\Rightarrow x+y=15$

Father's present age $=3(x+y)=3\times 15=45\text{years}$

Hence the present age of father is $45$ years.