A man buys 10 articles for ₹ 8 and sells them at the rate of ₹ 1.25 per article. His profit is

### Concept & Unitary Method for Profit To accurately determine profit or loss percentage, you must compare the Cost Price (CP) and Selling Price (SP) of an equal quantity of items. The easiest approach is to find the CP and SP of a single article. $$ \text{Profit \%} = \left(\frac{\text{SP of 1 unit} - \text{CP of 1 unit}}{\text{CP of 1 unit}}\right) \times 100 $$ ### Step-by-Step Solution * **Step 1:** Calculate the Cost Price (CP) of one article. * CP of 10 articles = ₹ 8 * CP of 1 article = $\frac{8}{10} = ₹ 0.80$ * **Step 2:** Identify the Selling Price (SP) of one article. * SP of 1 article is given as ₹ 1.25. * **Step 3:** Calculate the profit per article. * $\text{Profit} = \text{SP} - \text{CP} = 1.25 - 0.80 = ₹ 0.45$ * **Step 4:** Determine the profit percentage. * $\text{Profit \%} = \left(\frac{0.45}{0.80}\right) \times 100$ * Multiply numerator and denominator by 100 to remove decimals: $\left(\frac{45}{80}\right) \times 100$ * Simplify fraction by dividing by 5: $\left(\frac{9}{16}\right) \times 100$ * $\text{Profit \%} = \frac{900}{16} = \frac{225}{4}\%$ * Convert to mixed fraction: $225 \div 4 = 56$ with a remainder of 1. * $\text{Profit \%} = 56 \frac{1}{4}\%$ ### Exam Strategy & Shortcut You can also equalize the number of articles. Since CP is given for 10 articles (₹ 8), just find the SP for 10 articles. SP for 10 = $1.25 \times 10 = ₹ 12.50$. Profit = $12.50 - 8 = ₹ 4.50$. Profit \% = $\frac{4.50}{8} \times 100 = \frac{450}{8} = 56.25\%$, which is equal to $56 \frac{1}{4}\%$. ### Common Pitfall Misplacing the decimal point when finding the CP of one article (writing it as ₹ 1.25 or ₹ 0.08) is a common calculation error that derails the entire problem. ### Final Answer Therefore, the correct answer is **$56 \frac{1}{4}\%$**.