Question

The sum of the reciprocals of Meena’s ages (in years) 3 years ago and 5 years hence is `1/3`. Find her present ages.

Answer 1

Let the present age of Meena be x years

Meena’s age 3 years ago = (x – 3) years 

Meena’s age 5 years hence = (x + 5) years 

According to the given condition, 

`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) = 0 

⇒ (x – 7)(x + 3) = 0 

⇒ x – 7 = 0 or x + 3 = 0 

⇒ x = 7 or x = –3 

∴ x = 7   ...(Age cannot be negative)

Hence, the present age of Meena is 7 years.