# 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.

By Ritesh|Updated : November 13th, 2022

(a) 27 years and 5 years

(b) 38 years and 6 years

(c) 51 years and 7 years

(d) 30 years and 5 years

The present ages of both Asha and Nisha are 27 yr and 5 yr. Let Nisha be x years old at present time.

Then, according to the question Asha's present age = x2 + 2

Now, according to the question when Nisha grows to her mother's present age i.e., after (x2 + 2) - x yrs

Then, Asha's age also increased by [(x2 + 2) - x] yr

Again given that:

Age of Asha equals one year less than Nisha's current age.

It can be written in equations as:

(x2 + 2) + (x2 + 2) - x = 10x - 1

On computing the above equation we get:

2x2 - x + 4 = 10x - 1

2x2 - 11x + 5 = 0

The above equation can be written as:

2x2 - 10x - x + 5 = 0

Taking common we get:

2x (x - 5) - 1 (x - 5) = 0

(x - 5) (2x - 1) = 0

x = 5 or x = ½

[Here x = ½ cannot be possible, because at x = ½, Asha's age is 2 ¼ yr which is not possible]

Therefore, current age of Nisha = 5 yr

And according to the question current age of Asha = x2 + 2 = 52 + 2 = 25 + 2 = 27 yr

Summary:

## 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.

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. The present ages of both Asha and Nisha are 27 yr and 5 yr.