Profit and Loss — A man buys two hens for ₹ 500 each. He sells one at a 15% profit and the other at a 5% loss. What is his overall profit percentage on the combined cost?
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A5%
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B10%
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C15%
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D12%
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E2%
Answer
Correct Answer: 5%
Explanation
Introduction / Context: When costs are equal, the net percentage outcome equals (profit on item 1 − loss on item 2) divided by the combined cost. Because bases are the same (₹ 500 each), arithmetic is straightforward and avoids ratio traps.
Given Data / Assumptions:
- CP1 = CP2 = ₹ 500.
- Outcome 1: +15% ⇒ profit = 0.15 * 500 = 75.
- Outcome 2: −5% ⇒ loss = 0.05 * 500 = 25.
Concept / Approach: Net profit (rupees) = 75 − 25 = 50. Total cost = 500 + 500 = 1000. Overall profit% = 50/1000 * 100 = 5%.
Step-by-Step Solution:
Profit_1 = 0.15 * 500 = 75 Loss_2 = 0.05 * 500 = 25 Net profit = 75 − 25 = 50 Overall % = 50 / 1000 * 100 = 5%Verification / Alternative check: SP1 = 575; SP2 = 475; Total SP = 1050; Total CP = 1000 ⇒ 50 gain ⇒ 5%.
Why Other Options Are Wrong: 10%, 12%, and 15% overstate the net effect; 2% understates it.
Common Pitfalls: Averaging +15% and −5% to 5% works here only because CPs are equal; in general unequal bases require weighted averaging or rupee balancing.
Final Answer: 5%