Profit and Loss — A seller sells two tables at ₹ 1500 each. On one table he gains 20%, and on the other he loses 20%. What is the overall result on total cost: profit or loss, and by what percent?
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A4% loss
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B4% profit
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CNeither loss nor profit
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D10% loss
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E2% loss
Answer
Correct Answer: 4% loss
Explanation
Introduction / Context: Equal and opposite percentages on different cost bases do not cancel out when the selling prices are equal. This classic result shows that a 20% gain on one item and a 20% loss on another (sold at the same price) leads to a net loss.
Given Data / Assumptions:
- SP for both tables = ₹ 1500 each.
- Table 1: +20% profit; Table 2: −20% loss.
Concept / Approach: Recover CPs separately from SP = 1.20 * CP (profit case) and SP = 0.80 * CP (loss case). Sum CPs and compare with total SP to compute the overall percentage result on cost.
Step-by-Step Solution:
For +20%: 1500 = 1.20 * CP1 ⇒ CP1 = 1500 / 1.20 = 1250 For −20%: 1500 = 0.80 * CP2 ⇒ CP2 = 1500 / 0.80 = 1875 Total CP = 1250 + 1875 = 3125; Total SP = 3000 Net result = 3000 − 3125 = −125 ⇒ loss% = 125/3125 * 100 = 4%Verification / Alternative check: The “equal percentage gain & loss” rule around equal SPs always yields a loss because the higher CP in the loss case dominates.
Why Other Options Are Wrong: 4% profit and “neither” contradict the calculation; 10% or 2% loss are incorrect magnitudes.
Common Pitfalls: Averaging +20% and −20% to get 0%—invalid because bases (costs) differ.
Final Answer: 4% loss