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

Given:

Marks proportion in 6 papers = 5 : 6 : 7 : 8 : 9 : 10

Overall percentage = 60%

Formula used:

To find the number of papers in which the student received less than 60% marks, we will calculate the individual percentages based on the given proportions.

Calculation:

Let the total maximum marks for each paper be M.

Total marks scored = 5x + 6x + 7x + 8x + 9x + 10x = 45x

Overall score = 60% of total maximum marks = 60% of 6M = 0.6 × 6M = 3.6M

Given: 45x = 3.6M

⇒ x = 3.6M / 45 = M / 12.5

Now, calculate the marks in each paper:

Marks in Paper 1 = 5x = 5 × M / 12.5 = M / 2.5 = 40% of M

Marks in Paper 2 = 6x = 6 × M / 12.5 = 48% of M

Marks in Paper 3 = 7x = 7 × M / 12.5 = 56% of M

Marks in Paper 4 = 8x = 8 × M / 12.5 = 64% of M

Marks in Paper 5 = 9x = 9 × M / 12.5 = 72% of M

Marks in Paper 6 = 10x = 10 × M / 12.5 = 80% of M

Papers with less than 60% marks are Paper 1, Paper 2, and Paper 3.

∴ The student received less than 60% marks in 3 papers.