Question

A shopkeeper marks his goods in such a way that after allowing a discount of 25% on the marked price, he still makes a profit of 50%. Find the ratio of the C.P. to the M.P.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{C}.\mathrm{P}\mathrm{be}\mathrm{Rs}x\mathrm{and}\mathrm{M}.\mathrm{P}\mathrm{be}\mathrm{Rs}y. \\ \text{Gain\%}=50 \\ \mathrm{We}\mathrm{know}\mathrm{that}, \\ \mathrm{S}.\mathrm{P}=\left[\frac{\left(100+\mathrm{Gain}\%\right)}{100}\times \mathrm{C}.\mathrm{P}\right] \\ =\left[\frac{150}{100}\times x\right] \\ =\frac{3}{2}x \\ \mathrm{Discount}\%=25 \\ \mathrm{Discount}=25\%\mathrm{of}y \\ =\mathrm{Rs}0.25y \\ \mathrm{So},\mathrm{S}.\mathrm{P}=\mathrm{M}.\mathrm{P}-\mathrm{Discount} \\ =y-0.25y \\ =0.75y \\ \mathrm{So},\mathrm{S}.\mathrm{P}=0.75y \\ \mathrm{Also},\mathrm{S}.\mathrm{P}=\frac{3}{2}x \\ \text{Comparing both values for S.P., we get:} \\ \frac{3}{2}x=0.75y \\ \frac{x}{y}=\frac{0.75\times 2}{3} \\ =\frac{1.5}{3} \\ =\frac{1}{2} \\ \mathrm{Thus},\mathrm{C}.\mathrm{P}:\mathrm{M}.\mathrm{P}=1:2 \end{gathered}$$