A shopkeeper purchases 11 knives in ₹ 10 and sells them at the rate of 10 knives for ₹ 11. He earns a profit of

### Concept & Formula The core concept is calculating the cost price (CP) and selling price (SP) per unit to determine the overall profit percentage. $$Profit \% = \left( \frac{SP - CP}{CP} \right) \times 100$$ ### Step-by-Step Solution * **Given:** CP of 11 knives = ₹ 10, SP of 10 knives = ₹ 11. * **Calculation:** 1. Find CP of 1 knife: $CP = \frac{10}{11}$ 2. Find SP of 1 knife: $SP = \frac{11}{10}$ 3. Calculate Profit per knife = $SP - CP = \frac{11}{10} - \frac{10}{11} = \frac{121 - 100}{110} = \frac{21}{110}$ 4. Calculate Profit Percentage = $\left( \frac{21/110}{10/11} \right) \times 100 = \left( \frac{21}{110} \times \frac{11}{10} \right) \times 100$ 5. Simplify: $\frac{21}{100} \times 100 = 21\%$ ### Exam Strategy & Shortcut Cross-multiplication method for quantity and price: Buy: 11 (Qty) -> 10 (Price) Sell: 10 (Qty) -> 11 (Price) $CP = 10 \times 10 = 100$ $SP = 11 \times 11 = 121$ Profit = $121 - 100 = 21$ on a base of $100$, which is $21\%$. ### Common Pitfall A common mistake is calculating the profit percentage directly on the given aggregated quantities without finding the per-unit cost or using the cross-multiplication equalization method, leading to incorrect percentage bases. ### Final Answer Therefore, the correct answer is **21%**.