Difficulty: Medium
Correct Answer: 4% loss
Explanation:
Introduction / Context:Selling two items at the same selling price with equal profit and loss percentages leads to an overall loss, not break-even. This is a classic result due to different cost prices. We compute total cost and compare with total selling price.Given Data / Assumptions:
Concept / Approach:Compute the individual cost prices (CP) from SP and profit/loss percentage. Then sum the CPs to get total cost. Sum SPs to get total SP. Compare to find overall profit or loss percentage relative to total CP.Step-by-Step Solution:
For 20% profit: SP = 1.20 * CP ⇒ CP1 = 1500 / 1.20 = 1250.For 20% loss: SP = 0.80 * CP ⇒ CP2 = 1500 / 0.80 = 1875.Total CP = 1250 + 1875 = 3125.Total SP = 1500 + 1500 = 3000.Loss = 3125 − 3000 = 125.Loss % = 125 / 3125 * 100% = 4%.Verification / Alternative check:Equal and opposite percentages around the same SP do not cancel because the CPs are unequal; the product (1.20)*(0.80) = 0.96 shows a 4% net loss effect.
Why Other Options Are Wrong:
Common Pitfalls:Assuming profit and loss cancel to zero, or averaging the percentages arithmetically without considering different bases.
Final Answer:
4% loss
Discussion & Comments