Mohan took five papers in an examination, where each paper was of 250 marks. His marks in these papers were in the ratio 6 : 8 : 10 : 12 : 15. In all papers together, Mohan obtained 70% of the total marks, Then find the number of papers in which he got more than 80% marks.

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the total marks
Mohan took 5 papers, each of which is worth 250 marks. Therefore, the total marks for all papers combined is:
\[ \text{Total Marks} = 5 \times 250 = 1250 \]

### Step 2: Calculate the total marks obtained by Mohan
Mohan obtained 70% of the total marks. Thus, the marks he obtained can be calculated as:
\[ \text{Marks Obtained} = 70\% \text{ of } 1250 = \frac{70}{100} \times 1250 = 875 \]

### Step 3: Set up the ratio of marks
The marks Mohan obtained in the 5 papers are in the ratio of 6:8:10:12:15. Let's denote the marks in each paper as:
- Paper 1: \(6x\)
- Paper 2: \(8x\)
- Paper 3: \(10x\)
- Paper 4: \(12x\)
- Paper 5: \(15x\)

### Step 4: Calculate the total marks in terms of \(x\)
The total marks obtained can be expressed as:
\[ 6x + 8x + 10x + 12x + 15x = 51x \]

### Step 5: Set up the equation for total marks obtained
Since we know Mohan obtained 875 marks, we can set up the equation:
\[ 51x = 875 \]

### Step 6: Solve for \(x\)
To find \(x\), we divide both sides by 51:
\[ x = \frac{875}{51} \approx 17.14 \]

### Step 7: Calculate the marks in each paper
Now, we can calculate the marks obtained in each paper:
- Paper 1: \(6x = 6 \times 17.14 \approx 102.84\)
- Paper 2: \(8x = 8 \times 17.14 \approx 137.12\)
- Paper 3: \(10x = 10 \times 17.14 \approx 171.4\)
- Paper 4: \(12x = 12 \times 17.14 \approx 205.68\)
- Paper 5: \(15x = 15 \times 17.14 \approx 257.1\)

### Step 8: Determine the number of papers with more than 80% marks
To find out how many papers have more than 80% marks, we first calculate 80% of 250 marks:
\[ 80\% \text{ of } 250 = \frac{80}{100} \times 250 = 200 \]

Now, we check each paper:
- Paper 1: \(102.84 < 200\) (not more than 80%)
- Paper 2: \(137.12 < 200\) (not more than 80%)
- Paper 3: \(171.4 < 200\) (not more than 80%)
- Paper 4: \(205.68 > 200\) (more than 80%)
- Paper 5: \(257.1 > 200\) (more than 80%)

### Conclusion
Mohan scored more than 80% in 2 papers (Paper 4 and Paper 5).