Question

The sum of the reciprocals of Joseph's age 3 years ago and five years from now is `1/3` Find his present age.

Answer 1

Let present age of Joseph be x years.

It is given that the sum of the reciprocals of Joseph's age 3 years ago and five years from now is `1/3`.

⇒ `1/(1 - 3) + 1/(x + 5) = 1/3`

⇒ `((x + 5) + (x - 3))/((x - 3)(x + 5))`

⇒ `(2x + 2)/((x - 3)(x + 5)) = 1/3`

⇒ 3(2x + 2) = (x − 3)(x + 5)

⇒ 6x + 6 = x(x + 5) − 3(x + 5)

⇒ 6x + 6 = x² + 5x − 3x − 15

⇒ x² + 5x − 3x − 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

Since, age cannot be negative.

Hence, the present age of Joseph = 7 years.