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.…

Correct Option

Let the maximum marks for each paper be 100 units. Given there are 6 papers, the total maximum marks are $100 \times 6 = 600$100×6=600 units.

The student scored 60% overall. Therefore, the total marks obtained by the student are $\frac{60}{100} \times 600 = 360$10060​×600=360 units.

The marks obtained in the 6 papers are in the proportion of 5:6:7:8:9:10. Let the actual marks be $5x, 6x, 7x, 8x, 9x,$5x,6x,7x,8x,9x, and $10x$10x.

The sum of these individual marks must equal the total marks obtained:

$$5x + 6x + 7x + 8x + 9x + 10x = 360$$5x+6x+7x+8x+9x+10x=360

$$45x = 360$$45x=360

$$x = \frac{360}{45} = 8$$x=45360​=8

Substituting the value of $x$x, the marks obtained in each paper are:

• Paper 1: $5 \times 8 = 40$5×8=40
• Paper 2: $6 \times 8 = 48$6×8=48
• Paper 3: $7 \times 8 = 56$7×8=56
• Paper 4: $8 \times 8 = 64$8×8=64
• Paper 5: $9 \times 8 = 72$9×8=72
• Paper 6: $10 \times 8 = 80$10×8=80

The threshold for scoring less than 60% of the maximum marks in a single paper is $\frac{60}{100} \times 100 = 60$10060​×100=60 units.

Comparing the individual scores with this threshold:

• 40 is less than 60.
• 48 is less than 60.
• 56 is less than 60.
• 64 is not less than 60.
• 72 is not less than 60.
• 80 is not less than 60.

Thus, the student scored less than 60% of the maximum marks in 3 papers.

Incorrect Options

Options 1, 3, and 4 are incorrect. The detailed calculation demonstrates that the student scored less than 60% of the maximum marks in exactly 3 papers, which contradicts these options.