A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6:7:8:9:10. In all papers together, the candidate obtained 60% of the total marks then, the number of papers in which he got more than 50% marks is

Answer: Option C

Let the marks obtained in five subjects be 6x, 7x, 8x, 9x and 10x.
Total marks obtained = 40x
Max. Marks of the five subjects = $$\frac{40\text{x}}{0.6}$$   [40x is 60% of total marks]
Max. Marks in each subject = $$\frac{40\text{x}}{0.6\times 5}$$   = 13.33x
Hence, % of each subject = $$\frac{6\text{x}\times 100}{13.33}$$   = 45.01%
Or, $$\frac{7\text{x}\times 100}{13.33}$$   = 52.51
In same way other percentage are 60.01%, 67.52%, 75.01%.
Hence, number of subjects in which he gets more than 50% marks = 4