Question

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

Answer 1

Let the present age of Rehman be x years.

So, 3 years age his age was = (x – 3) years

The reciprocal = 1/(x - 3)

And, after 5 years the age will be = (x + 5) years

The reciprocal = 1/(x + 5)

So, according to the question

6x + 6 = x² + 2x – 15

x² + 2x – 6x – 15 – 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 and x = –3

x = – 3 is not possible because age cannot be negative.

So, x = 7

Therefore present age of Rehman is 7 years.