Profit and Loss – Two close profit rates reveal the cost price: A person sold a watch at a 10% profit. If he had sold it for ₹ 2000 more, the profit would have been 20%. What is the cost price of the watch?
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A₹ 15,000
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B₹ 10,000
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C₹ 20,000
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D₹ 25,000
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E₹ 18,000
Answer
Correct Answer: ₹ 20,000
Explanation
Introduction / Context:A fixed-amount increase in selling price moves the profit rate from 10% to 20%. Since both percentages refer to the same cost price, this gives a direct linear equation that can be solved quickly.
Given Data / Assumptions:
- Actual profit rate = 10%
- If SP increased by ₹ 2000 ⇒ profit rate = 20%
Concept / Approach:Let CP = x. Then SP at 10% is 1.10x. New SP for 20% would be 1.20x, which is ₹ 2000 more than 1.10x. Use this to find x.
Step-by-Step Solution:1.10x + 2000 = 1.20x2000 = 0.10x ⇒ x = ₹ 20,000
Verification / Alternative check:At CP ₹ 20,000: 10% SP = ₹ 22,000; 20% SP = ₹ 24,000; difference = ₹ 2000, confirming the condition.
Why Other Options Are Wrong:₹ 15,000, ₹ 10,000, ₹ 18,000, and ₹ 25,000 do not satisfy the exact ₹ 2000 gap between the two percentage-based SPs.
Common Pitfalls:Taking 10% and 20% of the selling price instead of cost price; the base is CP.
Final Answer:₹ 20,000