The average of five results is 46 and that of the first four is 45. The fifth results is : ?

Options

A. 1
B. 10
C. `12.5`
D. 50

Answer

To find the fifth result given the average of five results and the average of the first four results, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Average Formula**:
The average is calculated using the formula:
\[ \text{Average} = \frac{\text{Sum of terms}}{\text{Number of terms}} \]

2. **Calculate the Sum of the Five Results**:
We know the average of the five results is 46. Using the average formula:
\[ 46 = \frac{\text{Sum of 5 results}}{5} \]
To find the sum of the five results, we can rearrange the formula:
\[ \text{Sum of 5 results} = 46 \times 5 = 230 \]

3. **Calculate the Sum of the First Four Results**:
We know the average of the first four results is 45. Again, using the average formula:
\[ 45 = \frac{\text{Sum of 4 results}}{4} \]
Rearranging gives us:
\[ \text{Sum of 4 results} = 45 \times 4 = 180 \]

4. **Find the Fifth Result**:
Now, we can find the fifth result by subtracting the sum of the first four results from the sum of all five results:
\[ \text{Fifth result} = \text{Sum of 5 results} - \text{Sum of 4 results} \]
Substituting the values we calculated:
\[ \text{Fifth result} = 230 - 180 = 50 \]

5. **Conclusion**:
The fifth result is 50.