The mean of six numbers is 20. If one number is excluded, the mean is 15. Then the value of the excluded number is

Options

A. 40
B. 42
C. 45
D. 48

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given information
We know that the mean of six numbers is 20. This means that the sum of these six numbers can be calculated using the formula for the mean:

\[ \text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} \]

### Step 2: Calculate the sum of the six numbers
Using the mean, we can find the sum of the six numbers:

\[ \text{Sum of six numbers} = \text{Mean} \times \text{Number of values} = 20 \times 6 = 120 \]

### Step 3: Calculate the sum of the remaining five numbers
When one number (let's call it \( x_6 \)) is excluded, the mean of the remaining five numbers becomes 15. We can again use the mean formula to find the sum of these five numbers:

\[ \text{Sum of five numbers} = \text{Mean} \times \text{Number of values} = 15 \times 5 = 75 \]

### Step 4: Find the excluded number
Now, we can find the excluded number \( x_6 \) by subtracting the sum of the five numbers from the sum of the six numbers:

\[ x_6 = \text{Sum of six numbers} - \text{Sum of five numbers} = 120 - 75 = 45 \]

### Conclusion
The value of the excluded number is \( 45 \).

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