Question

Meena is twice as old as Soumya. If 6 years are subtracted from Meena's age and four years added to Soumya's age, then Soumya will be 4 times Meena's age. How old were they two years ago?
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Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Soumya}\mathrm{be}\mathrm{x}\mathrm{years}.\mathrm{Then}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Meena}=2\mathrm{x}\mathrm{years}. \\ \mathrm{Meena}\text{'}\mathrm{s}\mathrm{age}\mathrm{when}6\mathrm{years}\mathrm{are}\mathrm{subtracted}\mathrm{from}\mathrm{her}\mathrm{age}=\left(2\mathrm{x}-6\right)\mathrm{years}. \\ \mathrm{Soumya}\text{'}\mathrm{s}\mathrm{age}\mathrm{when}4\mathrm{years}\mathrm{are}\mathrm{added}\mathrm{to}\mathrm{her}\mathrm{age}=\left(\mathrm{x}+4\right)\mathrm{years}. \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question}: \\ \left(\mathrm{x}+4\right)=4\left(2\mathrm{x}-6\right) \\ \Rightarrow \mathrm{x}+4=8\mathrm{x}-24 \\ \mathrm{Subtracting}\mathrm{x}\mathrm{from}\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get} \\ 4=7\mathrm{x}-24 \\ \mathrm{Adding}24\mathrm{to}\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get} \\ 28=7\mathrm{x} \\ \Rightarrow 7\mathrm{x}=28 \\ \mathrm{Dividing}\mathrm{both}\mathrm{sides}\mathrm{by}7,\mathrm{we}\mathrm{have} \\ \mathrm{x}=\frac{28}{7}=4 \\ \mathrm{Therefore},\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{Soumya}\mathrm{is}4\mathrm{years},\mathrm{her}\mathrm{age}\mathrm{two}\mathrm{years}\mathrm{ago}=\left(4-2\right)=2\mathrm{years}. \\ \mathrm{Present}\mathrm{age}\mathrm{of}\mathrm{Meena}=2\mathrm{x}=2\left(4\right)=8\mathrm{years},\mathrm{her}\mathrm{age}\mathrm{two}\mathrm{years}\mathrm{ago}=\left(8-2\right)\mathrm{years}=6\mathrm{years}. \end{gathered}$$