100 oranges are bought at the rate of ₹ 350 and sold at the rate of ₹ 48 per dozen. The percentage of profit or loss is

### Concept & Profit Percentage To find the overall profit or loss percentage, we must compare the Cost Price (CP) and Selling Price (SP) for a single unit (or an equal number of units). $$ \text{Profit \%} = \left( \frac{\text{SP} - \text{CP}}{\text{CP}} \right) \times 100 $$ ### Step-by-Step Solution * **Step 1:** Calculate the Cost Price (CP) of a single orange. * CP of 100 oranges = ₹ 350 * CP of 1 orange = $\frac{350}{100} = ₹ 3.50$ * **Step 2:** Calculate the Selling Price (SP) of a single orange. * SP of 1 dozen (12 oranges) = ₹ 48 * SP of 1 orange = $\frac{48}{12} = ₹ 4.00$ * **Step 3:** Determine the profit. * Since SP > CP, there is a profit. * Profit = $4.00 - 3.50 = ₹ 0.50$ * **Step 4:** Calculate the profit percentage. * $\text{Profit \%} = \left( \frac{0.50}{3.50} \right) \times 100 = \left( \frac{1}{7} \right) \times 100$ * $\frac{100}{7}\% = 14 \frac{2}{7}\%$ ### Exam Strategy & Shortcut Instead of calculating for 1 unit, you can find the CP and SP for a common multiple, like 1200, or directly use ratios. The ratio of SP to CP per orange is $4 : 3.5$, which simplifies to $8 : 7$. A gain of 1 part on 7 parts is instantly recognizable as $\frac{1}{7} = 14 \frac{2}{7}\%$. ### Common Pitfall A frequent error is calculating the percentage on the Selling Price instead of the Cost Price, which would incorrectly yield $12.5\%$. Always ensure the denominator is the base Cost Price. ### Final Answer Therefore, the correct answer is **$14 \frac{2}{7}\%$ gain**.