If there is a profit of $20\%$ on the cost price of an article, the percentage of profit calculated on its selling price will be (S.S.C., 2010)

### Concept & Profit Margin Conversion Standard profit percentage is calculated on the Cost Price (CP). To find the profit percentage based on the Selling Price (SP), known as the profit margin, we use the formula: $$ \text{Profit on SP \%} = \left( \frac{\text{Profit}}{\text{SP}} \right) \times 100 $$ ### Step-by-Step Solution * Given: * Actual Profit = $20\%$ on Cost Price. * Let the Cost Price (CP) be 100. * Calculate Profit and Selling Price: * Profit = $20\%$ of 100 = 20. * $\text{SP} = \text{CP} + \text{Profit} = 100 + 20 = 120$. * Calculate the profit percent calculated on SP: * $\text{New Profit \%} = \left(\frac{\text{Profit}}{\text{SP}}\right) \times 100$ * $\text{New Profit \%} = \left(\frac{20}{120}\right) \times 100$ * $\text{New Profit \%} = \left(\frac{1}{6}\right) \times 100 = 16.66\% = 16\frac{2}{3}\%$ ### Exam Strategy & Shortcut Use fractions. A profit of $20\%$ on CP means a fraction of $\frac{1}{5}$. This means Profit = 1 unit, CP = 5 units. SP = CP + Profit = $5 + 1 = 6$ units. Profit on SP is $\frac{\text{Profit}}{\text{SP}} = \frac{1}{6}$. The percentage equivalent of $\frac{1}{6}$ is universally known as $16\frac{2}{3}\%$. ### Common Pitfall A common mistake is assuming profit on SP is always higher or identical to profit on CP. Since SP is generally larger than CP in a profitable transaction, the denominator increases, making the profit percentage on SP mathematically smaller. ### Final Answer Therefore, the correct answer is **$16\frac{2}{3}$**.