Question

Five years ago a man was seven times as old as his son. Five years hence, the father will be three times as old as his son. Find their present ages.

Answer 1

5 years ago,

Let age of son = x years

Then, age of father = 7x years

Present age of son = x + 5 years

and age of father = 7x + 5 years

5 years hence,

age of son = x + 5 + 5 = x + 10

and age of father = 7x + 5 + 5 = 7x + 10

According to the condition :

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

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

$\Rightarrow 7x-3x=30-10=20$

$\Rightarrow 4x=20$

$\Rightarrow x=\frac{20}{4}=5$

$\therefore$ Present age of son $=x+5=5+5=10$ years and

Age of father $=7x+5=7\times 5+5=35+5=40$ years