Question

Vishal's mother is 26 years older than him. If the product of their ages (in years) 3 years from now will be 360, then find the present age of Vishal and his mother.

Answer 1

Let the present age of Vishal be $x$ years.
Hence, his mother's present age will be $x+26$ years.

$3$ years from now,
Vishal's age = $x+3$ years
Age of his mother =$x+26+3=x+29$ years

As per hiven condition, the product of their ages $3$ years from now will be $360$, i.e.,
$(x+3)(x+29)=360$
$\Rightarrow x^2+29x+3x+87=360\Rightarrow x^2+32x+87-360=0$
$\Rightarrow x^2+32x-273=0$
$\Rightarrow x^2+39x-7x-273=0$
$\Rightarrow x(x+39)-7(x+39)=0$
$\Rightarrow (x+39)(x-7)=0$

Either $x+39=0\text{or}x-7=0$
$\Rightarrow x=-39\text{or}x=7$
As, the value of age cannot be, therefore $x=7$.

Hence, Vishal's present age = $7$ years and his mother's present age = $7+26=33$ years.