In a class of 50 students 10 have failed and their average marks are 28. The total marks obtained by the entire class are 2800. The average marks of those who have passed is

Options

A. 280
B. 2520
C. 63
D. None of these

Answer

To find the average marks of the students who have passed, we can follow these steps:

### Step 1: Identify the given information
- Total number of students = 50
- Number of students who failed = 10
- Average marks of students who failed = 28
- Total marks obtained by the entire class = 2800

### Step 2: Calculate the number of students who passed
The number of students who passed can be calculated as:
\[ \text{Number of students who passed} = \text{Total students} - \text{Students who failed} = 50 - 10 = 40 \]

### Step 3: Calculate the total marks obtained by the students who failed
Let the total marks obtained by the students who failed be \( x \). Since the average marks of the students who failed is 28, we can set up the equation:
\[ \text{Average} = \frac{\text{Total marks of failed students}}{\text{Number of failed students}} \implies 28 = \frac{x}{10} \]
From this, we can find \( x \):
\[ x = 28 \times 10 = 280 \]

### Step 4: Calculate the total marks obtained by the students who passed
The total marks obtained by the students who passed can be calculated as:
\[ \text{Total marks of passed students} = \text{Total marks of class} - \text{Total marks of failed students} = 2800 - 280 = 2520 \]

### Step 5: Calculate the average marks of the students who passed
The average marks of the students who passed can be calculated using the formula:
\[ \text{Average} = \frac{\text{Total marks of passed students}}{\text{Number of passed students}} = \frac{2520}{40} \]
Calculating this gives:
\[ \text{Average} = 63 \]

### Final Answer
The average marks of those who have passed is **63**.

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