Profit and Loss – Equal selling price again with ±5%: A man sells two houses for Rs 7.81 lakhs each. On one he gains 5% and on the other he loses 5%. What is the overall percentage effect on the whole sale?
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A0.25% loss
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B0.25% gain
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C2.5% loss
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DNo profit, no loss
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E1% loss
Answer
Correct Answer: 0.25% loss
Explanation
Introduction / Context:This is the same structure as the classic equal selling price with opposite percentage changes. The result is a small net loss given by a^2 / 100.
Given Data / Assumptions:
- SP1 = SP2 = Rs 7.81 lakhs
- One item at +5%, the other at -5%
Concept / Approach:For equal SP and opposite percentage of the same magnitude a, overall loss% = a^2 / 100.
Step-by-Step Solution:a = 5Loss% = 5^2 / 100 = 25 / 100 = 0.25%
Verification / Alternative check:Compute CP1 = SP / 1.05 and CP2 = SP / 0.95, then compare total CP with total SP; it will be a 0.25% loss.
Why Other Options Are Wrong:0.25% gain and no profit contradict the identity. 2.5% and 1% are wrong magnitudes.
Common Pitfalls:Assuming gains and losses cancel because they “average” to zero.
Final Answer:0.25% loss