Question

The sum of ages of a father and son is $45$ years. Five years ago the product of their ages was $4$ times the age of the father at that time. The present age of the father is

• A. $30$ yrs
• B. $31$ yrs
• C. $36$ yrs
• D. $41$ yrs

Answer 1

The correct option is C $36$ yrs

Let the present age of the father be $x$

$\therefore$ The present age of the son is $(45-x)$

Five years ago Age of father $=(x-5)$
Age of son $=\left(\right(45-x)-5)=(40-x)$

$\Rightarrow (x-5)(40-x)=4\times (x-5)$
$\Rightarrow 40x-200-x^2+5x=4x-20$
$\Rightarrow x^2-41x+180=0$
$\Rightarrow (x-36)(x-5)=0$

$\Rightarrow x=36$ or $x=5$ (Not possible)
$\therefore x=36$ years

$\therefore$ Present age of father $=36$ years

$\therefore$ Present age of son $=45-36=9$ years