The average of 20 numbers is calculated as 35. it is discovered later on that while calculating the average, one number, namely 85, was is read as 45. The correct average is :

Options

A. 36
B. 36.5
C. 37
D. 37.5

Answer

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

1. **Calculate the total sum of the 20 numbers based on the given average.**
- The average of the 20 numbers is given as 35.
- To find the total sum, we use the formula:
\[ \text{Total Sum} = \text{Average} \times \text{Number of items} \]
- Therefore, the total sum of the 20 numbers is:
\[ \text{Total Sum} = 35 \times 20 = 700 \]

2. **Identify the incorrect number and the correct number.**
- The incorrect number that was read is 45, and the correct number is 85.

3. **Adjust the total sum to account for the error.**
- Since 45 was incorrectly included instead of 85, we need to adjust the total sum:
- Subtract the incorrect number (45) and add the correct number (85):
\[ \text{Correct Total Sum} = 700 - 45 + 85 \]
- Calculating this gives:
\[ \text{Correct Total Sum} = 700 - 45 + 85 = 700 - 45 + 85 = 740 \]

4. **Calculate the correct average using the corrected total sum.**
- Now that we have the correct total sum, we can find the correct average:
\[ \text{Correct Average} = \frac{\text{Correct Total Sum}}{\text{Number of items}} = \frac{740}{20} \]
- Performing the division gives:
\[ \text{Correct Average} = 37 \]

Thus, the correct average of the 20 numbers is **37**.