Question

Product of Pragati’s age 2 years ago and 3 years hence is 84. Find her present age.

Answer 1

Let Pragati's present age be x years.
Her age 2 years ago = $x-2$
Her age 3 years hence = $x+3$
Product of Pragati’s age 2 years ago and 3 years hence is 84.
$$\begin{gathered} \left(x-2\right)\left(x+3\right)=84 \\ \Rightarrow x^2+x-6=84 \\ \Rightarrow x^2+x-90=0 \\ x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \Rightarrow x=\frac{-1\pm \sqrt{1^2-4\times 1\times \left(-90\right)}}{2} \\ =\frac{-1\pm \sqrt{361}}{2} \\ x=\frac{-1-19}{2}\mathrm{or}\frac{-1+19}{2} \\ \Rightarrow x=-10\mathrm{or}9 \end{gathered}$$
But age cannot be negative so, x = 9.
Thus, Pragati's present age is 9 years.