Let us say the present age of Rehman is x years.
Three years ago, Rehman’s age was (x – 3) years.
Five years after, his age will be (x + 5) years.
Given, the sum of the reciprocals of Rehman’s ages 3 years ago and after 5 years is equal to $\dfrac{1}{3}$.
∴ $ \dfrac{1}{x}-3 + \dfrac{1}{x}-5$ = $\dfrac{1}{3}$
$\dfrac{(x+5+x-3)}{(x-3)(x+5)}$ = $\dfrac{1}{3}$
$\dfrac{(2x+2)}{(x-3)(x+5)}$ =$\dfrac{1}{3}$
⇒ 3(2x + 2) = (x-3)(x+5)
⇒ 6x + 6 = $x^{2} + 2x – 15$
⇒ $x^{2} – 4x – 21$ = 0
⇒ $x^{2} – 7x + 3x – 21$ = 0
⇒ x(x – 7) + 3(x – 7) = 0
⇒ (x – 7)(x + 3) = 0
⇒ x = 7, -3
As we know, age cannot be negative.
Therefore, Rehman’s present age is 7 years.