Meena purchased two fans at ₹1,200 each. She sold one at a 5% loss and the other at a 10% gain. What is her overall percentage result (gain or loss) on the combined transaction?

Difficulty: Easy

Correct Answer: 2.5% profit

Explanation:


Introduction / Context:
When two items have equal costs but unequal gain/loss percentages, total result is found by summing individual selling prices and comparing to total cost. Here, both items cost ₹1,200, simplifying aggregation.


Given Data / Assumptions:

  • Fan A: CP = ₹1,200, sold at 5% loss ⇒ SP_A = 0.95 * 1,200 = ₹1,140.
  • Fan B: CP = ₹1,200, sold at 10% gain ⇒ SP_B = 1.10 * 1,200 = ₹1,320.
  • Total CP = ₹2,400.


Concept / Approach:
Total SP = SP_A + SP_B, then compute overall profit% = (Total SP − Total CP)/Total CP * 100.


Step-by-Step Solution:
Total SP = 1,140 + 1,320 = ₹2,460Overall profit = 2,460 − 2,400 = ₹60Overall profit% = 60 / 2,400 * 100 = 2.5%


Verification / Alternative check:
Since costs are equal, the average of the percentage gains/losses weighted by cost roughly indicates direction; here positive net because +10% outweighs −5% over equal bases.


Why Other Options Are Wrong:
1.2% profit/loss and 2.5% loss contradict the exact aggregation results.


Common Pitfalls:
Averaging 10% and −5% as 2.5% directly works only because costs are equal; otherwise, weighted averages are needed.


Final Answer:
2.5% profit

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