Question -
Answer -
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.