Question

Seven years ago, Vanin’s age was five times the square of swati’s age. Three years hence Swati’s age will be two fifth of Varun’s age. Find their present ages.

Answer 1

Seven years ago, let Swathi’s age be x years. 

Seven years ago, let Varun’s age was 5x² years.

Swathi’s present age = x + 7 years

Varun’s present age = (5x² + 7) years

3 years hence, we have Swathi’s age = x + 7 + 3 years

= x + 10 years

Varun’s age = 5x² + 7 + 3 years

= 5x² + 10 years

It is given that 3 years hence Swathi’s age will be 2/5 of Varun’s age.

∴ x + 10 = (2/5) (5x² + 10)

⇒ x + 10 = 2x² + 4

⇒ 2x² – x – 6 = 0

⇒ 2x(x – 2) + 3(x – 2) = 0

⇒ (2x + 3)(x – 2) = 0

⇒ x – 2 = 0

⇒ x = 2 (∵ 2x + 3 ≠ 0 as x > 0)

Hence Swathi’s present age = (2 + 7) years

= 9 years

Varun’s present age = (5 × 2 + 7) years = 27 years