4. The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age.

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. ∴ 1/x-3 + 1/x-5 = 1/3 (x+5+x-3)/(x-3)(x+5) = 1/3 (2x+2)/(x-3)(x+5) = 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.