An article was sold for ₹322, yielding a gain equal to one-sixth of the outlay (cost). Find the cost price of the article.
Aptitude
Profit and Loss
Difficulty: Easy
Choose an option
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A₹ 300
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B₹ 376
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C₹ 175
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D₹ 276
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E—
Answer
Correct Answer: ₹ 276
Explanation
Introduction / Context:“Gain equal to 1/6 of outlay” means the profit is 1/6 of cost price (CP). Therefore, selling price (SP) equals CP plus CP/6 = (7/6)CP. We invert this to find CP from the given SP.
Given Data / Assumptions:
- SP = ₹322.
- SP = (7/6) * CP.
Concept / Approach:Rearrange CP = SP * (6/7). This is a simple proportional relation.
Step-by-Step Solution:CP = 322 * (6/7) = 1932 / 7 = ₹276
Verification / Alternative check:Check: Profit = 322 − 276 = ₹46, which is 1/6 of 276 (since 276/6 = 46). Correct.
Why Other Options Are Wrong:₹300/₹376/₹175 do not satisfy SP = (7/6)CP with SP = ₹322.
Common Pitfalls:Using 1/6 of SP instead of CP; mishandling the fraction inversion when solving for CP.
Final Answer:₹ 276