Question

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

(a) 1 

(b) 3 

(c) 4 

(d) 5

Answer 1

(c) 4

Let the marks obtained in 5 subjects be 6x, 7x, 8x, 9x and 10x.

Average score = 60%

\(\therefore\) \(\frac{6X+7X+8X+9X+10X}{5}\) = \(\frac{60}{100}\) \(\Rightarrow\) \(\frac{40X}{5}\) = \(\frac{60}{100}\)

\(\Rightarrow\) x = \(\frac{60\times5}{100\times40}\) = \(\frac{3}{40}\) = 0.075

\(\therefore\) The marks are 0.45, 0.525, 0.6, 0.675 and 0.75, i.e., 45%, 52.5%, 60%, 67.5% and 75%

\(\therefore\) Number of papers in which the marks exceed 50% = 4.