At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.

Question

Philoid · Accepted Answer

Let Nisha’s age be x.

Then, Asha’s age = x² + 2

When Nisha grows to Asha’s present age, Asha’s age be one year less than 10 times that of Nisha’s present age i.e.,

(x² + 2) + [(x² + 2) – x] = 10x - 1

⇒ 2x² - 11x + 5 = 0

By using quadratic formula,

∴ For ,

Nisha’s age is 5 years.

Asha’s age will be 27 years.

∴ For ,

Nisha’s age is 1/2 years.

Asha’s age will be years. (not possible)