Question

A dealer gets Rs 56 less if instead of selling a chair at a gain of 15%, it is sold at a gain of 8%. Find the cost price of the chair.

Answer 1

$$\begin{gathered} \mathrm{Let}Rsxbethe\mathrm{CP}. \\ {\mathrm{Gain}}_1\mathrm{percentage}=\left(\frac{{\mathrm{gain}}_1}{\mathrm{CP}}\times 100\right)\% \\ \Rightarrow 15=\frac{{\mathrm{gain}}_1}{x}\times 100 \\ \Rightarrow {\mathrm{Gain}}_1=\mathrm{Rs}\frac{15x}{100} \\ \mathrm{Again},{\mathrm{gain}}_2\mathrm{percentage}=\left(\frac{{\mathrm{gain}}_2}{\mathrm{CP}}\times 100\right)\% \\ \Rightarrow 8=\frac{{\mathrm{gain}}_2}{x}\times 100 \\ \Rightarrow {\mathrm{Gain}}_2=\mathrm{Rs}\frac{8x}{100} \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question},\mathrm{we}\mathrm{have}: \\ {\mathrm{Gain}}_1-{\mathrm{gain}}_2=56 \\ \Rightarrow \frac{15\mathrm{x}}{100}-\frac{8\mathrm{x}}{100}=56 \\ \Rightarrow \frac{7\mathrm{x}}{100}=56 \\ \Rightarrow 7x=5600 \\ \Rightarrow x=800 \\ \mathrm{Hence},\mathrm{the}\mathrm{CP}\mathrm{of}\mathrm{the}\mathrm{chair}\mathrm{is}\mathrm{Rs}800. \end{gathered}$$