A student appeared in 6 papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion of 5 : 6 : 7 : 8 : 9 : 10. Overall he scored 60%. In how many number of papers did he score less than 60% of the maximum marks?

Let the maximum marks for each paper be 100. Then, the total maximum marks for 6 papers = 6 * 100 = 600. The student scored 60% overall. Overall score = 60% of 600 = (60/100) * 600 = 360 marks. The marks in the 6 papers are in the proportion 5 : 6 : 7 : 8 : 9 : 10. Let the actual marks be 5k, 6k, 7k, 8k, 9k, and 10k. The sum of these marks must equal the overall score: 5k + 6k + 7k + 8k + 9k + 10k = 360 45k = 360 k = 360 / 45 = 8 Now, we can find the marks obtained in each paper: Paper 1: 5k = 5 * 8 = 40 Paper 2: 6k = 6 * 8 = 48 Paper 3: 7k = 7 * 8 = 56 Paper 4: 8k = 8 * 8 = 64 Paper 5: 9k = 9 * 8 = 72 Paper 6: 10k = 10 * 8 = 80 The question asks in how many papers he scored less than 60% of the maximum marks for a single paper. 60% of the maximum marks (100) for a single paper = (60/100) * 100 = 60 marks. Now, we compare each paper's score with 60: * Paper 1 (40 marks) is less than 60. (Yes) * Paper 2 (48 marks) is less than 60. (Yes) * Paper 3 (56 marks) is less than 60. (Yes) * Paper 4 (64 marks) is not less than 60. (No) * Paper 5 (72 marks) is not less than 60. (No) * Paper 6 (80 marks) is not less than 60. (No) The student scored less than 60% of the maximum marks in 3 papers (Paper 1, Paper 2, and Paper 3). The final answer is B