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, let's break it down as follows:

### Step 1: Calculate the sum of all 20 numbers
The average of 20 numbers is given as 12. We can use the formula for average:

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

From this, we can rearrange to find the sum:

\[ \text{Sum of 20 numbers} = \text{Average} \times \text{Number of terms} = 12 \times 20 = 240 \]

### Step 2: Calculate the sum of the first 12 numbers
The average of the first 12 numbers is given as 11. Using the same formula:

\[ \text{Sum of first 12 numbers} = \text{Average} \times \text{Number of terms} = 11 \times 12 = 132 \]

### Step 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:

\[ \text{Sum of next 7 numbers} = \text{Average} \times \text{Number of terms} = 10 \times 7 = 70 \]

### Step 4: Calculate the sum of the first 19 numbers
Now we can find the sum of the first 19 numbers by adding the sums of the first 12 and the next 7 numbers:

\[ \text{Sum of first 19 numbers} = \text{Sum of first 12 numbers} + \text{Sum of next 7 numbers} = 132 + 70 = 202 \]

### Step 5: Calculate the last number
Finally, to find the last number, we subtract the sum of the first 19 numbers from the total sum of all 20 numbers:

\[ \text{Last number} = \text{Sum of 20 numbers} - \text{Sum of first 19 numbers} = 240 - 202 = 38 \]

### Conclusion
The last number is **38**.

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