Question

The product of Tanvy's age (in years) 5 years ago and her age 8 years later is 30. Find her present age.

Answer 1

$$\begin{gathered} \text{Let the present age of Meena be}x\text{years}\text{.} \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question}: \\ (x-5)(x+8)=30 \\ \Rightarrow x^2+3x-40=30 \\ \Rightarrow x^2+3x-70=0 \\ \Rightarrow x^2+(10-7)x-70=0 \\ \Rightarrow x^2+10x-7x-70=0 \\ \Rightarrow x(x+10)-7(x+10)=0 \\ \Rightarrow (x+10)(x-7)=0 \\ \Rightarrow x+10=0\text{or}x-7=0 \\ \Rightarrow x=-10\text{or}x=7 \\ \Rightarrow x=7(\because \text{Age cannot be negative}) \\ \mathrm{Thus}\text{, the present age of Meena is 7 years}\text{.} \end{gathered}$$