Question

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

Answer 1

Asha is 27 years old and Nisha is 5 years old.

Answer 2

Solution Explanation:
Let Nisha’s present age = $x$ years. Then, Asha’s present age = $x^2 + 2$ years (given).
The time needed for Nisha to become as old as Asha currently is:
  $T = (x^2 + 2) - x = x^2 - x + 2$ years.
At that time, Asha’s age will be:
  $x^2 + 2 + (x^2 - x + 2) = 2x^2 - x + 4$.
According to the condition, this future age of Asha is one year less than 10 times Nisha’s present age, i.e.,
  $2x^2 - x + 4 = 10x - 1$.
Rearranging, we get:
  $2x^2 - 11x + 5 = 0$.
Solving the quadratic,
  Discriminant $D = 121 - 40 = 81$,
  $x = \frac{11 \pm 9}{4}$.
Thus,
  $x = \frac{20}{4} = 5$ or $x = \frac{2}{4} = 0.5$.
Since ages are typically integers, we take $x = 5$.
So, Nisha’s present age = 5 years and Asha’s present age = $5^2 + 2 = 27$ years.