Question

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.

Answer 1

Let the present age of Rehman = x

∴ 3 years ago Rehman’s age = (x – 3) years

5 years later Rehman’s age = (x + 5) years

Now, according to the condition,

1/(x – 3 ) + 1/(x + 5) = 1/3 
(x + 5 + x – 3)/(x – 3)(x + 5) = 1/3 
(2x + 2)/(x² – 3x +5x – 15) = 1/3 
x² + 2x – 15 = 6x + 6 
x² – 4x – 21 = 0 
(x + 3)(x – 7) = 0

Either, x + 3 = 0 Or, x – 7 = 0

Thus, x = 7 or – 3; but age cannot be negative.

Hence the present age of Rehman is 7 years.