Profit and Loss — Rajan sells an article for ₹ 6000 at a loss of 25%. Determine the original Cost Price (CP) using SP = (1 − 25%) * CP and present the exact value.
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A₹ 7500
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B₹ 7200
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C₹ 8000
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D₹ 8500
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E₹ 7000
Answer
Correct Answer: ₹ 8000
Explanation
Introduction / Context: A stated loss% allows direct recovery of CP from a known SP by dividing SP by the remaining percentage factor. This is a basic yet essential transformation in profit-and-loss questions.
Given Data / Assumptions:
- SP = ₹ 6000
- Loss% = 25%
- Loss is on CP
Concept / Approach: With a 25% loss, SP = 0.75 * CP. Hence CP = SP / 0.75. Substitute and compute.
Step-by-Step Solution:
CP = 6000 / 0.75Compute: 6000 / 0.75 = 8000Therefore, CP = ₹ 8000Verification / Alternative check: Check forward: 25% of 8000 = 2000; SP = 8000 − 2000 = 6000, which matches the given SP.
Why Other Options Are Wrong: ₹ 7500, ₹ 7200, ₹ 8500, and ₹ 7000 fail to produce SP = ₹ 6000 when a 25% loss is applied to CP.
Common Pitfalls: Multiplying SP by 0.75 instead of dividing by 0.75, or mistakenly applying the percentage on SP rather than on CP.
Final Answer: ₹ 8000