By selling an article, a man makes a profit of $25\%$ of its selling price. His profit percent is (S.S.C., 2010)

### Concept & Converting Profit Base When profit is given as a percentage of the Selling Price (SP), you need to find the Cost Price (CP) to calculate the actual (real) profit percentage, which is always based on CP. $$ \text{Actual Profit \%} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 $$ ### Step-by-Step Solution * Given: * Profit = $25\%$ of SP. * Let the Selling Price (SP) be 100. * Calculate Profit: * Profit = $25\%$ of 100 = 25. * Determine Cost Price (CP): * $\text{CP} = \text{SP} - \text{Profit}$ * $\text{CP} = 100 - 25 = 75$. * Calculate the actual profit percent (on CP): * $\text{Profit \%} = \left(\frac{25}{75}\right) \times 100$ * $\text{Profit \%} = \left(\frac{1}{3}\right) \times 100 = 33.33\% = 33\frac{1}{3}\%$ ### Exam Strategy & Shortcut Use fractional equivalents. $25\% = \frac{1}{4}$. If profit is $\frac{1}{4}$ of SP, it means for every ₹ 4 of SP, profit is ₹ 1. So, CP = $4 - 1 = 3$. Actual profit percent on CP is $\frac{1}{3} \times 100 = 33\frac{1}{3}\%$. ### Common Pitfall Assuming the given $25\%$ profit on selling price is the same as the actual profit percentage. Always verify the base of the percentage. ### Final Answer Therefore, the correct answer is **$33\frac{1}{3}$**.