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.

• A. 27 years and 5 years
• B. 38 years and 6 years
• C. 51 years and 7 years
• D. 30 years and 5 years

Answer 1

The correct option is

A

27 years and 5 years

Let Nisha's present age be $x$ yr.
Then, Asha's present age = $x^2+2\left[bygivencondition\right]$
Now, when Nisha grows to her mother's present age i.e., after $(x^2+2)-xyrs.$ Then, Asha's age also increased by $\left[\right(x^2+2)-x]$ yr.
Again by given condition,
Age of Asha = One years less than 10 times the present age of Nisha
$(x^2+2)+(x^2+2)-x=10x-1$
$\Rightarrow 2x^2-x+4=10x-1$
$\Rightarrow 2x^2-11x+5=0$
$\Rightarrow 2x^2-10x-x+5=0$
$\Rightarrow 2x(x-5)-1(x-5)=0$
$\Rightarrow (x-5)(2x-1)=0$
$\therefore x=5$
[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 not possible]
Hence, required age of Nisha = 5 yr
And required age of Asha $=x^2+2=(5{)}^2+2=25+2=27$yr