**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.

**Solution:**

Let Nisha's present age be $x y r$.

Then, Asha's present age $=x^{2}+2$ [by given condition]

Now, when Nisha grows to her mother’s present age i.e., after [(x2 +2)- x] yr. Then, Asha’s age also increased by [(x2 + 2) – x]yr.

Again by given condition,

Age of Asha = One years less than 10 times the present age of Nisha

$\left(x^{2}+2\right)+\left\{\left(x^{2}+2\right)-x\right\}=10 x-1$

$\Rightarrow \quad 2 x^{2}-x+4=10 x-1$

$\Rightarrow \quad 2 x^{2}-11 x+5=0$

$\Rightarrow \quad 2 x^{2}-10 x-x+5=0$

$\Rightarrow \quad 2 x(x-5)-1(x-5)=0$

$\Rightarrow \quad(x-5)(2 x-1)=0$

$\therefore$ $x=5$

[here, $x=\frac{1}{2}$ cannot be possible, because at $x=\frac{1}{2}$, Asha's age is $2 \frac{1}{4}$ yr which is n $\alpha$ possible]

Hence, required age of Nisha = 5yr

and required age of Asha = x2 + 2 = (5)2 + 2 = 25 + 2 = 27 yr