Question

(4) The age of Reena and Tina are in the ratio 3 : 4. Five years ago their ages were in the ratio 2 : 3. Find their present ages.

Answer 1

Dear student

$$\begin{gathered} \mathrm{Let}\mathrm{ratio}\mathrm{coefficient}\mathrm{be}\mathrm{x}: \\ \mathrm{Given}:\mathrm{The}\mathrm{age}\mathrm{of}\mathrm{Reena}\mathrm{and}\mathrm{Tina}\mathrm{are}\mathrm{in}\mathrm{the}\mathrm{ratio}3:4 \\ \mathrm{So},\mathrm{Reena}\text{'}\mathrm{s}\mathrm{present}\mathrm{age}=3\mathrm{x}\mathrm{and}\mathrm{Tina}\text{'}\mathrm{s}\mathrm{present}\mathrm{age}=4\mathrm{x} \\ \mathrm{Five}\mathrm{years}\mathrm{ago}, \\ \mathrm{Reena}\text{'}\mathrm{s}\mathrm{age}=3\mathrm{x}-5\mathrm{and}\mathrm{Tina}\text{'}\mathrm{s}\mathrm{age}=4\mathrm{x}-5 \\ \mathrm{and}\mathrm{Given}:\mathrm{Five}\mathrm{years}\mathrm{ago}\mathrm{their}\mathrm{ages}\mathrm{were}\mathrm{in}\mathrm{the}\mathrm{ratio}2:3 \\ \mathrm{So},\frac{3\mathrm{x}-5}{4\mathrm{x}-5}=\frac{2}{3} \\ \Rightarrow 3(3\mathrm{x}-5)=2(4\mathrm{x}-5) \\ \Rightarrow 9\mathrm{x}-15=8\mathrm{x}-10 \\ \Rightarrow 9\mathrm{x}-8\mathrm{x}=-10+15 \\ \Rightarrow \mathrm{x}=5 \\ \mathrm{So},\mathrm{Reena}\text{'}\mathrm{s}\mathrm{present}\mathrm{age}=3\mathrm{x}=3\times 5=15\mathrm{years} \\ \mathrm{and}\mathrm{Tina}\text{'}\mathrm{s}\mathrm{present}\mathrm{age}=4\mathrm{x}=4\times 5=20\mathrm{years} \end{gathered}$$
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