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?

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 $5x,6x,7x,8x,9x,$ and $10x$.

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

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

$$45x=360$$

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

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.