Akhilesh took five papers in an examination , where each paper was of of 200 marks .his marks in these papers were in the proportion of `7:8:9:10:11` .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 :

Options

A. A)1
B. B)3
C. C)4
D. D)5

Answer

To solve the problem step by step, we will follow the given information and perform calculations accordingly.

### Step 1: Determine the total marks
Akhilesh took 5 papers, each of 200 marks. Therefore, the total marks for all papers combined is:
\[ \text{Total Marks} = 5 \times 200 = 1000 \]

### Step 2: Calculate the total marks obtained
Akhilesh obtained 60% of the total marks. Thus, we can calculate the marks he obtained as follows:
\[ \text{Marks Obtained} = 60\% \text{ of Total Marks} = \frac{60}{100} \times 1000 = 600 \]

### Step 3: Set up the ratio of marks
The marks obtained in the papers are in the ratio of \(7:8:9:10:11\). Let the marks in each paper be represented as:
- Paper A: \(7x\)
- Paper B: \(8x\)
- Paper C: \(9x\)
- Paper D: \(10x\)
- Paper E: \(11x\)

### Step 4: Write the equation for total marks
The total marks obtained can also be expressed in terms of \(x\):
\[ 7x + 8x + 9x + 10x + 11x = 600 \]
Combining the terms gives:
\[ 45x = 600 \]

### Step 5: Solve for \(x\)
Now, we can solve for \(x\):
\[ x = \frac{600}{45} = \frac{40}{3} \]

### Step 6: Calculate the marks in each paper
Now we can calculate the marks obtained in each paper:
- Paper A:
\[ 7x = 7 \times \frac{40}{3} = \frac{280}{3} \approx 93.33 \]
- Paper B:
\[ 8x = 8 \times \frac{40}{3} = \frac{320}{3} \approx 106.67 \]
- Paper C:
\[ 9x = 9 \times \frac{40}{3} = \frac{360}{3} = 120 \]
- Paper D:
\[ 10x = 10 \times \frac{40}{3} = \frac{400}{3} \approx 133.33 \]
- Paper E:
\[ 11x = 11 \times \frac{40}{3} = \frac{440}{3} \approx 146.67 \]

### Step 7: Determine the number of papers with more than 50% marks
Since each paper is out of 200 marks, 50% of 200 is:
\[ \text{50% of 200} = 100 \]
Now we check how many papers have marks greater than 100:
- Paper A: \(93.33 < 100\) (Not more than 50%)
- Paper B: \(106.67 > 100\) (More than 50%)
- Paper C: \(120 > 100\) (More than 50%)
- Paper D: \(133.33 > 100\) (More than 50%)
- Paper E: \(146.67 > 100\) (More than 50%)

### Conclusion
The number of papers in which Akhilesh scored more than 50% marks is:
\[ \text{Total Papers} = 4 \]

Thus, the answer is **4 papers**.

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