The average of 45 results was calculated as 27 but later it was found that while calculating 39 was taken as 93 by mistake, then what will be the correct average?

Options

A. 25.8
B. 26.8
C. 27.2
D. 28.2

Answer

To find the correct average after identifying the mistake in the calculation, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Total Marks Based on the Initial Average**:
- The average of 45 results is given as 27.
- To find the total marks, we use the formula:
\[ \text{Total Marks} = \text{Average} \times \text{Number of Results} \]
- Therefore, the total marks calculated is:
\[ \text{Total Marks} = 27 \times 45 = 1215 \]

**Hint**: Remember that the total marks can be found by multiplying the average by the number of results.

2. **Identify the Error in the Calculation**:
- It was found that instead of 39, 93 was taken.
- The difference between the incorrect and correct value is:
\[ \text{Difference} = 93 - 39 = 54 \]

**Hint**: To find the error, subtract the correct value from the incorrect value.

3. **Adjust the Total Marks**:
- Since 54 marks were added incorrectly, we need to subtract this from the total marks to get the correct total:
\[ \text{Correct Total Marks} = 1215 - 54 = 1161 \]

**Hint**: Adjust the total marks by subtracting the error amount to find the correct total.

4. **Calculate the Correct Average**:
- Now, we calculate the correct average using the corrected total marks:
\[ \text{Correct Average} = \frac{\text{Correct Total Marks}}{\text{Number of Results}} = \frac{1161}{45} \]
- Performing the division:
\[ \text{Correct Average} = 25.8 \]

**Hint**: To find the average, divide the corrected total marks by the number of results.

### Final Answer:
The correct average after adjusting for the mistake is **25.8**.