The average marks of 42 students in an examination, was 64. Later it was found that the marks of three students were misread as 72, 58 and 44 instead of the actual marks 64, 42 and 26 respectively. What is the correct average marks?

Options

A. 61
B. 62
C. 63
D. 60

Answer

To find the correct average marks after correcting the misread marks, we can follow these steps:

### Step 1: Calculate the total marks based on the initial average.
The average marks of 42 students is given as 64.

\[ \text{Total Marks} = \text{Number of Students} \times \text{Average Marks} \]
\[ \text{Total Marks} = 42 \times 64 = 2688 \]

### Step 2: Identify the misread and actual marks.
The misread marks of three students are:
- Misread: 72, 58, 44
- Actual: 64, 42, 26

### Step 3: Calculate the sum of the misread marks and the actual marks.
Sum of the misread marks:
\[ \text{Sum of Misread Marks} = 72 + 58 + 44 = 174 \]

Sum of the actual marks:
\[ \text{Sum of Actual Marks} = 64 + 42 + 26 = 132 \]

### Step 4: Adjust the total marks by removing the misread marks and adding the actual marks.
\[ \text{Corrected Total Marks} = \text{Total Marks} - \text{Sum of Misread Marks} + \text{Sum of Actual Marks} \]
\[ \text{Corrected Total Marks} = 2688 - 174 + 132 = 2646 \]

### Step 5: Calculate the correct average marks.
\[ \text{Correct Average} = \frac{\text{Corrected Total Marks}}{\text{Number of Students}} \]
\[ \text{Correct Average} = \frac{2646}{42} = 63 \]

Thus, the correct average marks of the students is **63**.