Question

A father tells his son, five years ago, I was seven times as old as you were. After five years from the present time, I will be three times as old as you will be. Find their present ages.

Answer 1

Let $x$ be the age of the son before 5 years.

Then age the father 5 years ago $=7x$

At present,

Age of son $=x+5$

Age of father $=7x+5$

5 years later from the present time:

Age of son $=x+5+5=x+10$

Age of father $=7x+5+5=7x+10$

It is given that, father is $3$ times as old as his son after 5 years from the present time.

$\Rightarrow 7x+10=3(x+10)$

$\Rightarrow 7x+10=3x+30$

$\Rightarrow 7x-3x=30-10$

$\Rightarrow 4x=20$

$x=\frac{20}{4}$

$\Rightarrow x=5$

The present age of son $=x+5=5+5=10$ years

The present age of father $=7x+5=7\left(5\right)+5=40$ years

$\therefore$ The father's age is 40 years and the son's age is 10 years old.