The average of five numbers is 496. If two of them are 117 and 140, find the average of remaining three numbers.

Options

A. 239
B. 717
C. 741
D. 637

Answer

To find the average of the remaining three numbers when the average of five numbers is given, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Total Sum of the Five Numbers:**
The average of the five numbers is 496. The formula for average is:
\[ \text{Average} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \]
Therefore, we can rearrange this to find the total sum:
\[ \text{Sum of all observations} = \text{Average} \times \text{Number of observations} \]
Substituting the values:
\[ \text{Sum of all observations} = 496 \times 5 = 2480 \]

2. **Sum of the Two Known Numbers:**
We know two of the numbers are 117 and 140. We can find their sum:
\[ \text{Sum of known numbers} = 117 + 140 = 257 \]

3. **Calculate the Sum of the Remaining Three Numbers:**
To find the sum of the remaining three numbers, we subtract the sum of the known numbers from the total sum:
\[ \text{Sum of remaining three numbers} = \text{Total sum} - \text{Sum of known numbers} \]
Substituting the values:
\[ \text{Sum of remaining three numbers} = 2480 - 257 = 2223 \]

4. **Calculate the Average of the Remaining Three Numbers:**
The average of the remaining three numbers can be calculated using the formula for average:
\[ \text{Average} = \frac{\text{Sum of remaining numbers}}{\text{Number of remaining numbers}} \]
Substituting the values:
\[ \text{Average} = \frac{2223}{3} = 741 \]

### Final Answer:
The average of the remaining three numbers is **741**.