Question

At present A vani's age is $2$ more than the square of her daughter Nitya's age. After $15$ years she will be $2$ to more than twice Nitya's age. Find their present ages.

Answer 1

Let Vani's Age be $V$

and Nitya's Age be $N$

Now, According to Question

At Present

$V=2+N^2.................\left(1\right)$

After 15 years

$V+15=2+2(N+15)................\left(2\right)$

Subtracting (2) from (1)

$N^2-2N-15=0\Rightarrow N^2-5N+3N-15=0\Rightarrow (N-5)(N+3)=0\Rightarrow N=5,-3$

Hence, $N=5$ (As age cannot be Negative)

and $V=2+N^2=2+5^2=2+25=27$