A student appeared in 6 papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion 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?

Method 1: No need of calculation, this question tests your basic logic.

Average marks is given and since all marks are unique (their proportions are given in increasing order), half would be below the average and half above it. so, 3 is our answer.

Method 2: Let total marks in each subject be 100. Total marks for all 6 subjects = 600

Overall marks scored = 60% of 600 = 360
Assuming the marks as per proportion and adding we get

5x + 6x + 7x + 8x + 9x + 10x = 360
=> 45x = 360 => x = 8

So, marks in the given 6 subjects –
5 × 8 = 40
6 × 8 = 48
7 × 8 = 56
8 × 8 = 64
9 × 8 = 72
10 × 8 = 80

Hence, in 3 subjects, the student has scored less than 60% marks.