Let us say, present age of Rahman 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 1/3.

∴ \(\frac{1}{x-3}+ {1}{x-5}= \frac{1}{3}\)

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

\(\frac{2x+2}{(x-3)(x+5)} = \frac{1}{3}\)

⇒ 3(2x + 2) = (x-3)(x+5)

⇒ 6x + 6 = x² + 2x – 15

⇒ x² – 4x – 21 = 0

⇒ x² – 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, Rahman’s present age is 7 years.