Question

two numbers are in the ratio of 3:5.if 5 is subtracted from each of the number,they become in the ratio of 1:2.find the numbers

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{two}\mathrm{numbers}\mathrm{are}x\mathrm{and}y \\ \mathrm{According}\mathrm{to}\mathrm{first}\mathrm{condition}: \\ \frac{x}{y}=\frac{3}{5} \\ \Rightarrow 5x-3y=0..........\left(1\right) \\ \mathrm{According}\mathrm{to}\mathrm{second}\mathrm{condition}: \\ \frac{x-5}{y-5}=\frac{1}{2} \\ \Rightarrow 2x-10=y-5 \\ \Rightarrow 2x-y=5..........\left(2\right) \\ \mathrm{Multiply}\left(2\right)\mathrm{by}3,\mathrm{we}\mathrm{get}, \\ 6x-3y=15...........\left(3\right) \\ \mathrm{Subtracting}\left(1\right)\mathrm{from}\left(3\right),\mathrm{we}\mathrm{get}, \\ \left(6x-3y\right)-\left(5x-3y\right)=15 \\ x=15 \\ \mathrm{From}\left(1\right),\mathrm{we}\mathrm{get}, \\ \Rightarrow 5\times 15-3y=0 \\ \Rightarrow 75-3y=0 \\ \Rightarrow -3y=-75 \\ \Rightarrow y=25 \\ \mathrm{So},\mathrm{the}\mathrm{two}\mathrm{numbers}\mathrm{are}15\mathrm{and}25. \end{gathered}$$