Question

find 2 numbers in the ratio 8:7such that when each is decreased by 12 and a half they are in the ratio 11:9

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}2\mathrm{numbers}\mathrm{be}\mathrm{a}\mathrm{and}\mathrm{b}. \\ \mathrm{Given}:\frac{\mathrm{a}}{\mathrm{b}}=\frac{8}{7}\Rightarrow \mathrm{a}=\frac{8\mathrm{b}}{7}...\left(1\right) \\ \mathrm{Also},\frac{\mathrm{a}-12.5}{\mathrm{b}-12.5}=\frac{11}{9} \\ \Rightarrow 9\mathrm{a}-112.5=11\mathrm{b}-137.5 \\ \Rightarrow 137.5-112.5=11\mathrm{b}-9\mathrm{a} \\ \Rightarrow 25=11\mathrm{b}-9\mathrm{a} \\ \Rightarrow 25=11\mathrm{b}-9\times \frac{8\mathrm{b}}{7}\left[\mathrm{using}\left(1\right)\right] \\ \Rightarrow 25=11\mathrm{b}-\frac{72\mathrm{b}}{7} \\ \Rightarrow 175=77\mathrm{b}-72\mathrm{b} \\ \Rightarrow 175=5\mathrm{b} \\ \Rightarrow \mathbf{b}\mathbf{=}\mathbf{35} \\ \mathrm{and}\mathrm{a}=\frac{8\times 35}{7}\left[\mathrm{using}\left(1\right)\right] \\ \mathbf{a}\mathbf{=}\mathbf{40} \end{gathered}$$
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