The average of 11 number is 10. When one number is eliminated, the average of the remaining numbers is 9.3. What is the eliminated number?

Answer

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

### Step 1: Calculate the total sum of the 11 numbers.
Given that the average of 11 numbers is 10, we can find the total sum (S) of these numbers using the formula for average:

\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Number of numbers}} \]

So, we have:

\[ 10 = \frac{S}{11} \]

Multiplying both sides by 11 gives:

\[ S = 10 \times 11 = 110 \]

### Step 2: Calculate the total sum of the remaining 10 numbers.
When one number (let's call it \( x \)) is eliminated, the average of the remaining 10 numbers is 9.3. We can find the total sum of the remaining numbers (S'):

\[ 9.3 = \frac{S'}{10} \]

Multiplying both sides by 10 gives:

\[ S' = 9.3 \times 10 = 93 \]

### Step 3: Set up the equation to find the eliminated number.
The total sum of the remaining numbers (S') can also be expressed in terms of the total sum (S) and the eliminated number (x):

\[ S' = S - x \]

Substituting the values we found:

\[ 93 = 110 - x \]

### Step 4: Solve for the eliminated number \( x \).
Rearranging the equation gives:

\[ x = 110 - 93 \]

Calculating this gives:

\[ x = 17 \]

### Conclusion
The eliminated number is \( 17 \).

---