Question

If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than 5 times her actual age. What is her age now?

Answer 1

Let, the present age of Zeba be x years.
If she were 5 years younger, then the square of her age would have been 11 more than 5 times her actual age
$$\begin{gathered} \Rightarrow {\left(x-5\right)}^2=11+5x \\ \Rightarrow x^2+25-10x=11+5x \\ \Rightarrow x^2-15x+14=0 \\ \Rightarrow x^2-14x-x+14=0 \\ \Rightarrow x\left(x-14\right)-1\left(x-14\right)=0 \\ \Rightarrow \left(x-14\right)\left(x-1\right)=0 \\ \Rightarrow x=14\mathrm{or}x=1 \end{gathered}$$
The age cannot be 1 year as we have also talked about the age 5 years ago.
Therefore, Zeba's present age is $x=14$ years.