The average marks of 40 students in an examnation was 25. It was later found that the marks of one student had been wrongly entered as 73 instead of 37.What is the value of correct average?

Options

A. `24.3`
B. `24.1`
C. `24.5`
D. `24.7`

Answer

To find the correct average marks of the 40 students after correcting the mistake in one student's marks, we can follow these steps:

### Step 1: Calculate the total marks based on the given average.
The average marks of the 40 students is given as 25. We can calculate the total marks (Σx) using the formula:

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

Substituting the values:

\[ \text{Total Marks} = 25 \times 40 = 1000 \]

### Step 2: Identify the incorrect and correct marks.
The marks of one student were wrongly entered as 73 instead of 37. Therefore, we need to adjust the total marks by removing the incorrect entry and adding the correct one.

### Step 3: Adjust the total marks.
To find the correct total marks, we will subtract the incorrect marks and add the correct marks:

\[ \text{Correct Total Marks} = \text{Total Marks} - \text{Incorrect Marks} + \text{Correct Marks} \]

Substituting the values:

\[ \text{Correct Total Marks} = 1000 - 73 + 37 \]

Calculating this gives:

\[ \text{Correct Total Marks} = 1000 - 73 + 37 = 1000 - 36 = 964 \]

### Step 4: Calculate the correct average.
Now, we can find the correct average by dividing the corrected total marks by the number of students:

\[ \text{Correct Average} = \frac{\text{Correct Total Marks}}{\text{Number of Students}} = \frac{964}{40} \]

Calculating this gives:

\[ \text{Correct Average} = 24.1 \]

### Final Answer:
The correct average marks of the 40 students is **24.1**.

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