Let the present age of Rehman be x years.
3 years ago Rehman’s age = x – 3 and its reciprocal is \(\frac{1}{x-3}\)
Rehman’s age 5 years from now = x + 5 and its reciprocal is \(\frac{1}{x+5}\)
The sum of the reciprocals
⇒ x2 + 2x – 15 = 3(2x + 2)
⇒ x2 + 2x – 15 = 6x + 6
⇒ x2 + 2x – 15 – 6x – 6 = 0
⇒ x2 – 4x – 21 =0
⇒ x2 – 7x + 3x – 21 =0
⇒ x(x – 7) + 3(x – 7) 0
⇒ (x – 7) (x + 3) = 0
⇒ x – 7 = 0 or x + 3 = 0
⇒ x = 7 or x = -3
But x can’t be negative, x = 7
i.e., Present age of Rehman = 7 years.
