Question

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:

• A. 2
• B. 3
• C. 4
• D. 5

Hint:

Always calculate each paper's percentage individually when marks are in ratio form and total percentage is given.

Answer 1

The Correct Option is B

Let the maximum marks for each paper be $M$. Marks obtained are in ratio 6:7:8:9:10, so total marks obtained = $6k + 7k + 8k + 9k + 10k = 40k$.
Total maximum marks = $5M$.
We are told $\frac{40k}{5M} = 0.60 \Rightarrow 40k = 3M \Rightarrow k = \frac{3M}{40}$.
Marks in each paper: Paper 1: $\frac{18M}{40} = 45%$ (less than 50%)
Paper 2: $\frac{21M}{40} = 52.5%$ (more than 50%)
Paper 3: $\frac{24M}{40} = 60%$ (more than 50%)
Paper 4: $\frac{27M}{40} = 67.5%$ (more than 50%)
Paper 5: $\frac{30M}{40} = 75%$ (more than 50%)
Thus, papers 2, 3, 4, and 5 have more than 50% marks. But total is 4 — wait, check: We must see candidate got exactly 60% overall, hence counts papers above 50%. From calculation above, we have **4** above 50%. Correction — the answer is (3) 4.