Question

Product of Shraddha’s age 2 years ago and 3 years hence is 84. Find her present age.

Answer 1

Let Shraddha’s present age be x years.

2 years ago her age was (x – 2) years.

3 years hence her age will be (x + 3) years.

From the given condition,

(x – 2) × (x + 3) = 84

∴ x² + x – 6 = 84

∴ x² + x – 6 – 84 = 0

∴ x² + x – 90 = 0 

∴ x² + 10x – 9x – 90 = 0

∴ x(x + 10) – 9(x + 10) = 0

∴ (x + 10) (x – 9) = 0

∴ x + 10 = 0 or x – 9 = 0

∴ x = –10 or x = 9

But the age cannot be negative.

∴ x = –10 is unacceptable.

∴ x = 9

Shraddha’s present age is 9 years.