Question

A cycle merchant allows 20% discount on the marked price of the cycles and still makes a profit of 20%. If he gains Rs 360 over the sale of one cycle, find the marked price of the cycle.

Answer 1

$$\begin{gathered} \mathrm{Given}, \\ Gainononecycle=\mathrm{Rs}.360 \\ \mathrm{Gain}=20\% \\ \mathrm{Gain}\%=\frac{\mathrm{Gain}}{\mathrm{CP}}\times 100 \\ 20=\frac{360}{\mathrm{CP}}\times 100 \\ \mathrm{CP}=\mathrm{Rs}.1800 \\ \mathrm{SP}=\frac{100+\mathrm{Gain}\%}{100}\times \mathrm{CP} \\ \mathrm{SP}=\frac{120}{100}\times 1800=\mathrm{Rs}.2160 \\ \mathrm{SP}=\mathrm{Rs}.2160 \\ \mathrm{Discount}=20\% \\ \mathrm{MP}=\frac{100\times \mathrm{SP}}{100-\mathrm{Discount}\%} \\ \mathrm{MP}=\frac{100\times 2160}{80}=\mathrm{Rs}.2700 \\ \mathrm{Hence},theMPofonecycleis\mathrm{Rs}.2700. \end{gathered}$$