Difficulty: Easy
Correct Answer: 33 1/3
Explanation:
Introduction / Context: Here we again have a ratio based profit and loss question involving identical items. The relationship between selling price of 6 bananas and cost price of 8 bananas directly leads to the profit percentage without needing actual rupee amounts.
Given Data / Assumptions:
Concept / Approach: Let cost price per banana be C and selling price per banana be S. Given 6S = 8C. From this relationship we find S in terms of C. Profit per banana is S - C. Profit percentage is (S - C) / C * 100. Because the quantities differ, there will be a profit, not a loss, as selling price per piece will be greater than cost price per piece.
Step-by-Step Solution: Let CP per banana = C, SP per banana = S. Given 6S = 8C. Divide both sides by 2: 3S = 4C. So S = (4/3)C. Profit per banana = S - C = (4/3)C - C = (1/3)C. Profit percentage = [(1/3)C / C] * 100 = (1/3)*100 ≈ 33 1/3%.
Verification / Alternative check: Assume C = Rs 3. Then S = (4/3)*3 = Rs 4. Cost of 8 bananas = 8 * 3 = Rs 24. Selling price of 6 bananas = 6 * 4 = Rs 24, which matches the condition. Profit per banana = 4 - 3 = Rs 1 and profit percentage = (1 / 3) * 100 ≈ 33.33%, confirming the answer.
Why Other Options Are Wrong: 20%, 25%, and 30% come from miscalculations or confusion about which quantity is larger. The ratio 6 : 8 simplifies to 3 : 4 and directly leads to the fraction 1/3 for profit on cost. Only 33 1/3% is consistent.
Common Pitfalls: A typical error is to invert the ratio and write 6C = 8S, which leads to a loss. Another error is to think that profit percentage is (8 - 6)/8 * 100, which ignores the fact that the equation involves price, not quantity alone. Always express SP and CP per unit before computing percentage.
Final Answer: The seller makes a profit of 33 1/3 percent.
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