MAT Exam 2025 Paper

Concept:Use the first discount and profit relation to find the ratio of cost price to marked price, then apply the new discount to find the new profit percentage.Explanation:Let the marked price be $MP$ and the cost price be $CP$.At a $25\%$ discount, the selling price is:$$SP = MP\left(1-\frac{25}{100}\right)=\frac{3}{4}MP$$Since the profit is $27.5\%$, we also have:$$SP = CP\left(1+\frac{27.5}{100}\right)=\frac{255}{200}CP$$Equating the two expressions for $SP$:$$\frac{3}{4}MP=\frac{255}{200}CP$$$$\frac{CP}{MP}=\frac{3}{4}\times\frac{200}{255}=\frac{10}{17}$$Now, with the new discount of $20\%$, the new selling price is:$$SP_{new}=MP\left(1-\frac{20}{100}\right)=\frac{4}{5}MP$$New profit percentage is:$$\frac{SP_{new}-CP}{CP}\times100=\left(\frac{SP_{new}}{CP}-1\right)\times100$$Substituting $SP_{new}=\frac{4}{5}MP$ and $\frac{MP}{CP}=\frac{17}{10}$:$$\left(\frac{4}{5}\times\frac{17}{10}-1\right)\times100$$$$=\left(\frac{68}{50}-1\right)\times100=36\%$$Answer:The shopkeeper now earns a profit of $36\%$.Correct option: D. $36\%$