#### 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.

5, 27

Solution

Let Nisha’s present age = x

At present Asha is 2 more than the square of Nisha’s age.

Hence, Asha present age = x2 + 2

According to question

x2 + 2 - x = 10x – 1 - ( x2 + 2 )

x2 + 2 – x = 10x – 1 – x2 - 2

x2 + 2 – x - 10x + x2 + 3=0

2x2-11x+5=0

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

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

$x=5,\frac{1}{2}$?

If Nisha’s age is 5

Asha age = (5)2+2=27

If Nisha’s age is 1/2  then Asha’s age is 2.25  which is not possible.