Loss-to-cost recovery: Niraj sells an article for ₹ 9,549 incurring a loss of 55%. Determine the original cost price of the article.
Aptitude
Profit and Loss
Difficulty: Easy
Choose an option
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A₹ 27,700
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B₹ 25,600
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C₹ 21,220
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D₹ 29,000
Answer
Correct Answer: ₹ 21,220
Explanation
Introduction / Context:When loss% is known with the selling price, the cost price can be found by dividing by the remaining percentage factor because SP = (1 − loss%) * CP.
Given Data / Assumptions:
- SP = ₹ 9,549.
- Loss = 55% ⇒ SP = 0.45 * CP.
Concept / Approach:Rearrange SP = 0.45 * CP to CP = SP / 0.45 and compute directly.
Step-by-Step Solution:CP = 9,549 / 0.45 = ₹ 21,220
Verification / Alternative check:Check: 45% of 21,220 is 9,549; hence SP at 55% loss equals 21,220 − 11,671 = 9,549, verifying the relationship (or directly 0.45 * 21,220 = 9,549).
Why Other Options Are Wrong:
- ₹ 27,700 / ₹ 25,600 / ₹ 29,000: result from dividing by the wrong factor or arithmetic slips.
Common Pitfalls:
- Treating 55% of SP rather than of CP as the loss base.
Final Answer:₹ 21,220