At present asha's age is 2 …

Let the present age of Nisha be x years.
Then, as per given condition
Asha's age (in years) is 2 more than the square of her daughter Nisha's age.
So, Asha's age = x² + 2
Difference in their ages = x² + 2 - x
And,  Asha's age when Nisha's age will be (x² + 2) years  = ( x² + 2) + (x² + 2 - x)
If Asha's age is one year less than 10 times the present age of Nisha = 10x - 1
So, As per given condition
(x² + 2 - x) + (x² + 2) = 10x - 1
$\Rightarrow$ 2x² - x + 4 = 10x - 1
$\Rightarrow$ 2x² - 11x + 5 = 0
$\Rightarrow$ 2x² - 10x - x + 5 = 0
$\Rightarrow$ 2x(x - 5) - 1(x - 5) = 0
$\Rightarrow$ (x - 5)(2x - 1) = 0
$\Rightarrow$ x - 5 = 0 or 2x - 1 = 0
$\Rightarrow$ x = 5 or $x = \frac{1}{2}$
$\Rightarrow$ x = 5 [as age can't be a fraction]
$\Rightarrow$ x² + 2 = 5² + 2 = 27
Hence, Nisha's age is 5 years and Asha's age is 27 years.