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 the Rehman’s current age = x years
Therefore, 3 years ago, age = x -3 years
and, after 5 years, age = x + 5 years
according to questions,

1/x -3 + 1/x + 5 = 1/3
⇒ (x +5) + (x – 3)/(x – 3)(x +5) = 1/3
⇒ 2x + 2/x² + 2x – 15 = 1/3
⇒ x² + 2x – 15 = 6x + 6
⇒ x² – 4x – 21 = 0
For the quadratic equation x² – 4x – 21 = 0, we have a = 1, b = – 4 and c = – 21.
Therefore, b² – 4ac = (-4)² – 4 × 1 × (-21) = 16 + 84 = 100 > 0
Hence, x = 4±√100/2 = 4±10/2 [As x = (-b±√(b²-4ac))/2a]
Either x = 4+10/2 = 14/2 = 7 or x = 4 -10/2 = – 6/2 = – 3
Age of person can’t be negative, so Rehman’s age = 7 years.