Question

The sum of the reciprocals of Rehamans ages, (in years) $3$ years ago and $5$ years to now is $\frac{1}{3}$. Find his present age.

Answer 1

Let, Rehamans present age $=x$

Rehamans age $3$ years ago $=x-3$

Rehamans age $5$ years from now $=x+5$

So,

$\begin{array}{c}\frac{1}{x-3}+\frac{1}{x+5}=\frac{1}{3}\\ \frac{x+5+x-3}{\left(x-3\right)\left(x+5\right)}=\frac{1}{3}\\ 3\left(2x+2\right)=\left(x-3\right)\left(x+5\right)\\ 6x+6=x^2+2x-15\\ x^2-4x-21=0\\ x^2-7x+3x-21=0\\ \left(x-7\right)\left(x+3\right)=0\\ x=7,x=-3\end{array}$

As age cannot be negative.

So,

$x=7$

Thus present age of Rehaman is $7$ years.