Question

If two numbers are in the ratio 5:7 and if 3 is subtracted from each of them, the ratio becomes 2:3, then the numbers are - A. 15 and 21, B. 30 and 42, C. 10 and 14, D. None of these

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{numbers}\mathrm{be}\mathrm{x}\mathrm{and}\mathrm{y} \\ \mathrm{Given},\frac{\mathrm{x}}{\mathrm{y}}=\frac{5}{7} \\ \Rightarrow 7\mathrm{x}=5\mathrm{y} \\ \Rightarrow \mathrm{x}=\frac{5\mathrm{y}}{7}..\left(1\right) \\ \mathrm{A}.\mathrm{T}.\mathrm{Q} \\ \Rightarrow \frac{\mathrm{x}-3}{\mathrm{y}-3}=\frac{2}{3} \\ \Rightarrow 3\mathrm{x}-9=2\mathrm{y}-6 \\ \Rightarrow 3\mathrm{x}-2\mathrm{y}=9-6 \\ \Rightarrow 3\mathrm{x}-2\mathrm{y}=3 \\ \Rightarrow 3\left(\frac{5\mathrm{y}}{7}\right)-2\mathrm{y}=3 \\ \Rightarrow \frac{15\mathrm{y}}{7}-2\mathrm{y}=3 \\ \Rightarrow 15\mathrm{y}-14\mathrm{y}=21 \\ \Rightarrow \mathrm{y}=21 \\ \Rightarrow \mathrm{x}=\frac{5\mathrm{y}}{7}\Rightarrow \mathrm{x}=\frac{5\times 21}{7}=15 \\ \mathrm{So}\mathrm{the}\mathrm{numbers}\mathrm{are}\mathrm{x}=15\mathrm{and}\mathrm{y}=21 \end{gathered}$$