The mean of 6 numbers is 20. If one number is deleted, their mean is 15. The deleted number is

Options

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

Answer

To find the deleted number, we can follow these steps:

### Step 1: Calculate the sum of the 6 numbers
Given that the mean of 6 numbers is 20, we can use the formula for the mean:

\[ \text{Mean} = \frac{\text{Sum of numbers}}{\text{Total numbers}} \]

Let the sum of the 6 numbers be \( S \). Therefore, we have:

\[ 20 = \frac{S}{6} \]

Multiplying both sides by 6 gives:

\[ S = 20 \times 6 = 120 \]

### Step 2: Calculate the sum of the remaining 5 numbers after deletion
When one number is deleted, the mean of the remaining 5 numbers is 15. Let the sum of the remaining 5 numbers be \( S' \). Using the mean formula again:

\[ 15 = \frac{S'}{5} \]

Multiplying both sides by 5 gives:

\[ S' = 15 \times 5 = 75 \]

### Step 3: Find the deleted number
Let the deleted number be \( x \). We know:

\[ S = S' + x \]

Substituting the values we found:

\[ 120 = 75 + x \]

To find \( x \), we can rearrange the equation:

\[ x = 120 - 75 = 45 \]

### Conclusion
The deleted number is **45**.

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