Marked price vs cost when sale at 3/4th MRP gives 25% gain: By selling an article at three-quarters of its marked price, a trader gains 25%. What is the ratio of the marked price to the cost price?
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A5 : 3
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B3 : 5
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C3 : 4
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D4 : 3
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E6 : 5
Answer
Correct Answer: 5 : 3
Explanation
Introduction / Context: Relate selling price to both MRP and cost via given fractions and gain. With sale at 3/4 of marked price and a 25% profit on cost, equate these two expressions for the same selling price to connect M and C directly as a ratio.
Given Data / Assumptions:
- Marked price = M.
- Selling price S = (3/4)M.
- Profit = 25% ⇒ S = 1.25C.
Concept / Approach: Set (3/4)M = 1.25C ⇒ M/C = (1.25)/(0.75) = (5/4)/(3/4) = 5/3. Express as a clean ratio M : C = 5 : 3.
Step-by-Step Solution:
(3/4)M = 1.25C.M/C = 1.25 / 0.75 = 5/3.Therefore M : C = 5 : 3.Verification / Alternative check: Let C = 3, then M = 5, S = (3/4)*5 = 3.75; profit = 0.75 = 25% of 3.
Why Other Options Are Wrong: 3:5, 3:4, 4:3, 6:5 contradict the relationship (3/4)M = 1.25C.
Common Pitfalls: Mixing which percentage applies to M or to C; remember profit is on cost, discount is on marked price.
Final Answer: 5 : 3