Discount given, profit achieved: A shopkeeper sells a book at a 10% discount on its marked price yet makes a 20% profit. What is the ratio of cost price to marked price?
Aptitude
Discount
Difficulty: Easy
Choose an option
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A6 : 5
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B5 : 6
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C3 : 4
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D2 : 3
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E4 : 5
Answer
Correct Answer: 3 : 4
Explanation
Introduction / Context:Two simple relations define selling price: SP = 0.90*MP (due to 10% discount) and SP = 1.20*CP (due to 20% profit). Equating them yields CP : MP directly.
Given Data / Assumptions:
- Discount = 10% ⇒ SP = 0.90 * MP
- Profit = 20% ⇒ SP = 1.20 * CP
Concept / Approach:Equate SP expressions to connect CP and MP, then simplify to a ratio in the lowest terms.
Step-by-Step Solution:
0.90*MP = 1.20*CP CP / MP = 0.90 / 1.20 = 3 / 4 Hence, CP : MP = 3 : 4Verification / Alternative check:Let CP = 3k, MP = 4k ⇒ SP = 0.9*4k = 3.6k, profit = 3.6k − 3k = 0.6k, which is 20% of 3k.
Why Other Options Are Wrong:Other ratios do not satisfy the simultaneous conditions implied by both discount and profit.
Common Pitfalls:Mixing the order (MP : CP instead of CP : MP). Always match the requested ratio.
Final Answer:3 : 4