Question

two numbers are such that the ratio between them is 5:7. if 7 is added to each of them , the ratio becomes 3:4 find the numbers

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{two}\mathrm{numbers}\mathrm{be}5\mathrm{x}\mathrm{and}7\mathrm{x}. \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}: \\ \frac{5\mathrm{x}+7}{7\mathrm{x}+7}=\frac{3}{4} \\ \Rightarrow 3\left(7\mathrm{x}+7\right)=4\left(5\mathrm{x}+7\right) \\ \Rightarrow 21\mathrm{x}+21=20\mathrm{x}+28 \\ \Rightarrow 21\mathrm{x}-20\mathrm{x}=28-21 \\ \Rightarrow \mathrm{x}=7 \\ \mathrm{Now},\mathrm{the}\mathrm{numbers}\mathrm{are}: \\ 5\mathrm{x}=5\times 7=35 \\ 7\mathrm{x}=7\times 7=49 \end{gathered}$$