Question

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

Answer 1

Let the present age of Rehman $=x$

$3$ years ago Rehman’s age $=(x–3)$ years

$5$ years later Rehman’s age $=(x+5)$ years.

Now, according to the condition,

$\frac{1}{(x–3)}+\frac{1}{(x+5)}=\frac{1}{3}$

$\frac{(x+5+x–3)}{(x–3)(x+5)}=\frac{1}{3}$

$\frac{(2x+2)}{(x^2–3x+5x–15)}=\frac{1}{3}$

$x^2+2x–15=6x+6$

$x^2–4x–21=0$

$(x+3)(x–7)=0$

Either,$x+3=0$ Or, $x–7=0$

Thus, $x=7$ or $–3$; but age cannot be negative.

Hence the present age of Rehman is $7$ years.