By selling an article for ₹ 100, a man gains ₹ 15. Then, his gain % is

### Concept & Profit Percentage Basics Profit percentage is always calculated based on the Cost Price (CP), not the Selling Price (SP). $$ \text{Cost Price (CP)} = \text{Selling Price (SP)} - \text{Gain} $$ $$ \text{Gain \%} = \left(\frac{\text{Gain}}{\text{CP}}\right) \times 100 $$ ### Step-by-Step Solution * **Step 1:** Extract the given values. * Selling Price (SP) = ₹ 100 * Gain = ₹ 15 * **Step 2:** Calculate the Cost Price (CP). * $\text{CP} = \text{SP} - \text{Gain}$ * $\text{CP} = 100 - 15 = ₹ 85$ * **Step 3:** Calculate the Gain Percentage. * $\text{Gain \%} = \left(\frac{15}{85}\right) \times 100$ * Simplify the fraction: $\frac{15}{85} = \frac{3}{17}$ * $\text{Gain \%} = \left(\frac{3}{17}\right) \times 100 = \frac{300}{17}\%$ * **Step 4:** Convert the improper fraction to a mixed number. * $300 \div 17 = 17$ with a remainder of $11$. * $\text{Gain \%} = 17 \frac{11}{17}\%$ ### Exam Strategy & Shortcut Realize immediately that the CP is $100 - 15 = 85$. You are looking for $\frac{15}{85}$, which reduces to $\frac{3}{17}$. Since $\frac{1}{17}$ is roughly $5.88\%$, $\frac{3}{17}$ is just under $18\%$. Only one option matches this logical deduction. ### Common Pitfall The most common mistake here is mistakenly calculating the percentage based on the Selling Price: $\frac{15}{100} \times 100 = 15\%$. Option (a) is a trap designed specifically for this error. ### Final Answer Therefore, the correct answer is **$17 \frac{11}{17}\%$**.