The average of 20 numbers is 12 . The average of the first 12 numbers is 11 and that of the next 7 numbers is 10 . The last number is

Options

A. 40
B. 38
C. 48
D. 50

Answer

To solve the problem step by step, we will follow the information given about the averages and calculate the last number accordingly.

### Step-by-Step Solution:

1. **Calculate the Total Sum of 20 Numbers:**
- The average of 20 numbers is given as 12.
- The formula for average is:
\[ \text{Average} = \frac{\text{Sum of all numbers}}{\text{Total number of observations}} \]
- Therefore, the sum of 20 numbers can be calculated as:
\[ \text{Sum} = \text{Average} \times \text{Total number of observations} = 12 \times 20 = 240 \]

2. **Calculate the Sum of the First 12 Numbers:**
- The average of the first 12 numbers is given as 11.
- Using the same formula for average:
\[ \text{Sum of first 12 numbers} = 11 \times 12 = 132 \]

3. **Calculate the Sum of the Next 7 Numbers:**
- The average of the next 7 numbers is given as 10.
- Again, using the average formula:
\[ \text{Sum of next 7 numbers} = 10 \times 7 = 70 \]

4. **Calculate the Sum of the First 19 Numbers:**
- Now, we can find the sum of the first 19 numbers by adding the sums we calculated:
\[ \text{Sum of first 19 numbers} = \text{Sum of first 12 numbers} + \text{Sum of next 7 numbers} = 132 + 70 = 202 \]

5. **Calculate the Last Number:**
- We know the total sum of all 20 numbers is 240. To find the last number, we subtract the sum of the first 19 numbers from the total sum:
\[ \text{Last number} = \text{Total sum} - \text{Sum of first 19 numbers} = 240 - 202 = 38 \]

### Final Answer:
The last number is **38**.

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