A man buys an article for $10\%$ less than its value and sells it for $10\%$ more than its value. His gain or loss percent is

### Concept & Value vs Cost Price When an article is bought at a discount relative to its "value" and sold at a premium relative to the same "value", the profit percentage must be calculated on the discounted Cost Price, not the baseline value. ### Step-by-Step Solution * Given: * Cost Price (CP) = Value - $10\%$ of Value * Selling Price (SP) = Value + $10\%$ of Value * Let the intrinsic Value of the article be 100. * Calculate Cost Price (CP): * $\text{CP} = 100 - (10\% \text{ of } 100) = 100 - 10 = 90$ * Calculate Selling Price (SP): * $\text{SP} = 100 + (10\% \text{ of } 100) = 100 + 10 = 110$ * Calculate actual Gain: * $\text{Gain} = \text{SP} - \text{CP} = 110 - 90 = 20$ * Calculate Gain Percentage: * $\text{Gain \%} = \left(\frac{\text{Gain}}{\text{CP}}\right) \times 100$ * $\text{Gain \%} = \left(\frac{20}{90}\right) \times 100$ * $\text{Gain \%} = \frac{200}{9}\% = 22.22\%$ * Evaluate against options: * $22.22\%$ is strictly more than $20\%$. ### Exam Strategy & Shortcut If you buy at a $10\%$ discount and sell at a $10\%$ markup on a base of 100, your CP is 90 and SP is 110. Your absolute profit is 20. If your CP was 100, your profit would be exactly $20\%$. Since your CP (90) is *less* than 100, dividing the same profit margin (20) by a smaller base mathematically results in a percentage *greater* than $20\%$. No exact calculation is needed. ### Common Pitfall A classic trap is to assume that a $10\%$ drop on purchase and a $10\%$ increase on sale relative to a base value cancel out, or that they sum exactly to a $20\%$ profit. Always normalize back to the actual Cost Price. ### Final Answer Therefore, the correct answer is **more than $20\%$ profit**.