At present Asha’s age (in years) is 2 more

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