A student took five papers in an examination, where full marks were same on each paper. Her marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all these papers together, the candidate obtained 60% of the total marks. Then the num…

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Concept & Proportional Thresholds: To compare proportional marks to a percentage threshold, we must establish a relationship between the "ratio parts" of the marks obtained and the "maximum marks" per paper. Threshold = Percentage × Maximum Marks per Paper Step-by-Step Solution: 1. Define Obtained Marks: Let the marks obtained in the five papers be 6x, 7x, 8x, 9x, and 10x. 2. Calculate Total Obtained Marks: Total marks obtained = 6x + 7x + 8x + 9x + 10x = 40x. 3. Define Maximum Marks: Let the maximum marks for each single paper be M. Total maximum marks for all 5 papers = 5M. 4. Equate Using Given Percentage: The total marks obtained (40x) is 60% of the total maximum marks (5M). 40x = 0.60 × 5M 40x = 3M M = (40x/3) \approx 13.33x. 5. Determine the 50% Threshold: We need to find papers where marks are greater than 50% of M. 50% of M = 0.5 × (40x/3) = (20x/3) \approx 6.67x. 6. Compare Marks to Threshold: We check which papers have marks > 6.67x: - Paper 1: 6x (Less) - Paper 2: 7x (More) - Paper 3: 8x (More) - Paper 4: 9x (More) - Paper 5: 10x (More) She scored more than 50% in 4 papers. Exam Strategy & Shortcut: Ignore variables. Assume the sum of the ratio parts (40) is exactly the total marks obtained. Since 40 represents 60% of the grand total, the grand total is (40/0.6) = 66.67. Since there are 5 identical papers, the maximum marks per paper is (66.67/5) = 13.33. 50% passing threshold per paper = (13.33/2) = 6.67. Looking at the ratio numbers (6, 7, 8, 9, 10), the numbers 7, 8, 9, 10 are greater than 6.67. Thus, 4 papers. Common Pitfall: Attempting to calculate the average of the ratio numbers directly without tying them to the maximum possible marks, leading to arbitrary and incorrect threshold comparisons. Final Answer: Therefore, the correct answer is 4.

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