Maximum discount for break-even: A merchant initially marks goods up by 40% above cost. Approximately what maximum percentage discount on the marked price will result in no profit and no loss?
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A60%
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B28.5%
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C33.5%
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DNo discount
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E40%
Answer
Correct Answer: 28.5%
Explanation
Introduction / Context:Break-even occurs when SP = CP. Starting from a markup, apply a discount d so that the final selling price equals cost. Solve for d as a fraction of the marked price (MP).
Given Data / Assumptions:
- MP = 1.40 * CP (40% markup).
- We need SP = CP after discount d% on MP.
Concept / Approach:SP = MP * (1 − d). For break-even: MP * (1 − d) = CP ⇒ (1 − d) = CP / MP = 1 / 1.40.
Step-by-Step Solution:
1 − d = 1 / 1.40 = 0.714285... d = 1 − 0.714285... = 0.285714... ≈ 28.57% Approximate maximum discount ≈ 28.5% (to break even).Verification / Alternative check:Let CP = 100 ⇒ MP = 140. With a 28.57% discount, SP ≈ 140*0.7143 = 100, as required.
Why Other Options Are Wrong:33.5% overshoots and causes a loss; 60% is far too high; “No discount” ignores the markup; 40% would lead to a loss.
Common Pitfalls:Confusing percentage of cost with percentage of marked price when discounting.
Final Answer:28.5%