Question

The sum of the reciprocals of Varun's age (in years) 3 years ago and 5 years from now is `1/3`. Find his present age.

Answer 1

Let the varun's present age be x years

According to the question,

`1/(x - 3) + 1/(x + 5) = 1/3`

`(x + 5 + x - 3)/((x - 3)(x + 5)) = 1/3`

`(2x + 2)/(x^2 + 2x - 15) = 1/3`

x² + 2x – 15 = 6x + 6

x² – 4x – 21 = 0

x² – 7x + 3x – 21 = 0

x(x – 7) + 3(x – 7) = p

(x – 7)(x + 3) = 0

if x – 7 = 0, x = 7

if x + 3 = 0, x = – 3

Age can not be negative

∴ x = 7

Hence Varun's age be 7 years.