Find the marked price: An article costs ₹450. A shopkeeper allows a 10% discount to customers and still gains 20%. What is the marked price?
Aptitude
Discount
Difficulty: Easy
Choose an option
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A₹ 600
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B₹ 540
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C₹ 660
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D₹ 580
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E₹ 620
Answer
Correct Answer: ₹ 600
Explanation
Introduction / Context:Given CP and both discount and profit requirements, we compute the necessary marked price (MP). The selling price must satisfy both relations simultaneously: SP = 0.90*MP and SP = 1.20*CP.
Given Data / Assumptions:
- CP = ₹450
- Discount = 10% ⇒ SP = 0.90 * MP
- Profit = 20% ⇒ SP = 1.20 * CP = ₹540
Concept / Approach:Equate SP from both expressions and solve for MP: 0.90*MP = 540 ⇒ MP = 600.
Step-by-Step Solution:
SP (from profit) = 1.20 * 450 = 540 0.90 * MP = 540 ⇒ MP = 540 / 0.90 = ₹600Verification / Alternative check:With MP = 600, a 10% discount gives SP = 540, which is 20% above 450.
Why Other Options Are Wrong:₹540 is the SP, not MP; ₹660, ₹580, ₹620 do not satisfy 0.90*MP = 540.
Common Pitfalls:Using 10% of CP instead of 10% of MP for discounting.
Final Answer:₹ 600