Correct Option

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

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

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

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

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

$45 x = 360$

$x = \frac{360}{45} = 8$

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

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

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