The average of six numbers is 36. If one number is excluded, the average becomes 37. What is the excluded number?

Options

A. 37
B. 36
C. 35.5
D. 31

Answer

To solve the problem, we need to find the excluded number when the average of six numbers is given as 36, and the average becomes 37 when one number is excluded.

### Step-by-Step Solution:

1. **Calculate the Sum of Six Numbers:**
The average of six numbers is given as 36. The formula for average is:
\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Number of terms}} \]
Therefore, the sum of the six numbers can be calculated as:
\[ \text{Sum} = \text{Average} \times \text{Number of terms} = 36 \times 6 = 216 \]

2. **Calculate the Sum of the Remaining Five Numbers:**
When one number (let's call it \( x \)) is excluded, the average of the remaining five numbers becomes 37. Thus, the sum of the five numbers can be calculated as:
\[ \text{Sum of 5 numbers} = \text{Average} \times \text{Number of terms} = 37 \times 5 = 185 \]

3. **Set Up the Equation:**
We know that the sum of the six numbers is equal to the sum of the five numbers plus the excluded number \( x \):
\[ 216 = 185 + x \]

4. **Solve for the Excluded Number \( x \):**
Rearranging the equation to find \( x \):
\[ x = 216 - 185 = 31 \]

5. **Conclusion:**
The excluded number is \( 31 \).

### Final Answer:
The excluded number is **31**.