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A shopkeeper sells two articles for ₹1200 each. On the first article, he makes a profit of 20%, and on the second article, he incurs a loss of 20%. What is the overall profit or loss percentage in the entire transaction? A. 4% profit B. 4% loss C. No profit, no loss D. 2% loss
Correct Answer: Option B Let $SP_1$ be the selling price of the first article and $SP_2$ be the selling price of the second article. Given, $SP_1 = \text{₹}1200$ and $SP_2 = \text{₹}1200$. **Step 1: Calculate the Cost Price ($CP_1$) of the first article.** The shopkeeper makes a profit of 20% on the first article. If Profit% is 20%, then $SP_1 = CP_1 \times (1 + \frac{20}{100}) = CP_1 \times 1.20$. So, $CP_1 = \frac{SP_1}{1.20} = \frac{1200}{1.20} = \frac{12000}{12} = \text{₹}1000$. **Step 2: Calculate the Cost Price ($CP_2$) of the second article.** The shopkeeper incurs a loss of 20% on the second article. If Loss% is 20%, then $SP_2 = CP_2 \times (1 - \frac{20}{100}) = CP_2 \times 0.80$. So, $CP_2 = \frac{SP_2}{0.80} = \frac{1200}{0.80} = \frac{12000}{8} = \text{₹}1500$. **Step 3: Calculate the Total Selling Price (Total SP) and Total Cost Price (Total CP).** Total SP = $SP_1 + SP_2 = \text{₹}1200 + \text{₹}1200 = \text{₹}2400$. Total CP = $CP_1 + CP_2 = \text{₹}1000 + \text{₹}1500 = \text{₹}2500$. **Step 4: Determine the overall profit or loss.** Since Total CP (₹2500) > Total SP (₹2400), there is an overall loss in the transaction. Overall Loss Amount = Total CP - Total SP = ₹2500 - ₹2400 = ₹100. **Step 5: Calculate the overall profit or loss percentage.** Overall Loss Percentage = $ (\frac{\text{Overall Loss Amount}}{\text{Total CP}}) \times 100\% $ Overall Loss Percentage = $ (\frac{100}{2500}) \times 100\% = (\frac{1}{25}) \times 100\% = 4\% $ loss. Alternatively, for situations where two articles are sold at the same selling price, and one is sold at x% profit and the other at x% loss, there is always an overall loss given by the formula: Loss% = $ (\frac{x}{10})^2 \% $ In this case, x = 20. Loss% = $ (\frac{20}{10})^2 \% = (2)^2 \% = 4\% $ loss. The final answer is 4% loss.
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