When CP of 20 equals SP of 15 — compute profit percentage If the cost price of 20 articles equals the selling price of 15 articles (same type), find the profit percentage.
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A33 1/2 %
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B33 1/3 %
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C33 1/5 %
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D33 1/7 %
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E25 %
Answer
Correct Answer: 33 1/3 %
Explanation
Introduction / Context:Total cost equaling total revenue for different counts reveals the SP/CP ratio per unit. This directly gives profit percentage without needing explicit rupee values.
Given Data / Assumptions:
- 20 * CP per unit = 15 * SP per unit.
- Identical items with uniform unit prices.
Concept / Approach:From 20C = 15S ⇒ S/C = 20/15 = 4/3. Profit% = (S − C)/C * 100 = (4/3 − 1)*100 = 1/3*100.
Step-by-Step Solution:S/C = 4/3.Profit fraction = 1/3.Profit% = 33 1/3 %.
Verification / Alternative check:Let C = ₹3 ⇒ S = ₹4. Then 20C = ₹60 and 15S = ₹60 (consistent). Profit per unit = ₹1 on ₹3 ⇒ 33 1/3%.
Why Other Options Are Wrong:33 1/2%, 33 1/5%, 33 1/7% and 25% do not match the exact 4/3 ratio.
Common Pitfalls:Inverting the ratio to 3/4 or claiming loss instead of profit.
Final Answer:33 1/3 %