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 sum of their present ages.

Answer 1

Let nisha's present age be $x$,
Asha's present age $=x^2+2$
When Nisha turns her mother's age, $x^2+2-x$ years have passed. Asha's age $=10x-1$
$\Rightarrow x^2+2-x$ = $10x-1-[x^2+2]$
$\Rightarrow {2x}^2-11x+5=0$
$\Rightarrow (x-5)\ast (2x+1)=0$
$\Rightarrow (x-5)=0$ or $(2x+1)=0$
$\Rightarrow x=5$ or $x=\frac{-1}{2}$
Since age can not be negative,
$x=5$ is the right answer.
Nisha's age is $5$, Asha's age is $27$

Sum of their present ages $=5+27=32$