The average of 19 results is 111. If the average of first 10 results is 82 and that of the last 10 results is 129, then what will be the 10 result?

Options

A. 0
B. 1
C. 82
D. 111

Answer

To solve the problem, we need to find the 10th result based on the given averages. Let's break it down step by step.

### Step 1: Calculate the sum of all 19 results
The average of 19 results is given as 111. The sum of the results can be calculated using the formula:

\[ \text{Sum of results} = \text{Average} \times \text{Number of results} \]

So, the sum of all 19 results is:

\[ \text{Sum of 19 results} = 111 \times 19 = 2109 \]

### Step 2: Calculate the sum of the first 10 results
The average of the first 10 results is given as 82. Using the same formula:

\[ \text{Sum of first 10 results} = 82 \times 10 = 820 \]

### Step 3: Calculate the sum of the last 10 results
The average of the last 10 results is given as 129. Again, using the formula:

\[ \text{Sum of last 10 results} = 129 \times 10 = 1290 \]

### Step 4: Set up the equation to find the 10th result
The 10th result is included in both the first 10 results and the last 10 results. Therefore, we can express the relationship as follows:

\[ \text{Sum of first 10 results} + \text{Sum of last 10 results} - \text{10th result} = \text{Sum of 19 results} \]

Let \( x \) be the 10th result. Then we can write:

\[ 820 + 1290 - x = 2109 \]

### Step 5: Solve for the 10th result
Now, we can rearrange the equation to find \( x \):

\[ 2110 - x = 2109 \]

Adding \( x \) to both sides and subtracting 2109 from both sides gives:

\[ 2110 - 2109 = x \]

Thus,

\[ x = 1 \]

### Conclusion
The 10th result is \( 1 \).

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