A man sells two articles for ₹ 240 each. On one he gains $20\%$ and on the other he loses $20\%$. What is the gain or loss percent in the entire transaction? (S.S.C., 2005)

### Concept & Identical Selling Price Theorem When two articles are sold for the exact same selling price, and one is sold at a profit of $x\%$ while the other is sold at a loss of $x\%$, the overall transaction always results in a net loss. $$ \text{Net Loss } \% = \frac{x^2}{100} $$ ### Step-by-Step Solution * We are given that both articles are sold at the same price: $SP_1 = SP_2 = 240$. * The gain on the first article is $x = 20\%$. * The loss on the second article is $x = 20\%$. * Because the selling prices are equal and the percentage gain and loss are equal in magnitude, we can apply the standard theorem. * The transaction yields an overall loss. * $\text{Loss } \% = \frac{(20)^2}{100}$ * $\text{Loss } \% = \frac{400}{100} = 4\%$ ### Exam Strategy & Shortcut Commit the formula $\frac{x^2}{100}\%$ loss to memory. The actual selling price (₹ 240) is completely unnecessary information. As soon as you see "sells two articles for the same price" and "gains $20\%$ and loses $20\%$", immediately calculate $20 \times \frac{20}{100} = 4\%$ loss. ### Common Pitfall Assuming that a $20\%$ gain and a $20\%$ loss cancel each other out, resulting in a $0\%$ net change (no profit, no loss). This happens if the Cost Prices were equal, not the Selling Prices. ### Final Answer Therefore, the correct answer is **$4\%$ loss**.