The average of 20 numbers is 15 and the average of first five is 12.The average of the rest is

Options

A. 16
B. 15
C. 14
D. 13

Answer

To find the average of the remaining numbers after the first five, we can follow these steps:

### Step 1: Calculate the sum of all 20 numbers.
The average of 20 numbers is given as 15. The formula for average is:

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

From this, we can express the sum of the 20 numbers:

\[ \text{Sum of 20 numbers} = \text{Average} \times \text{Total numbers} = 15 \times 20 = 300 \]

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

\[ \text{Sum of first 5 numbers} = \text{Average} \times \text{Total numbers} = 12 \times 5 = 60 \]

### Step 3: Calculate the sum of the remaining 15 numbers.
To find the sum of the remaining numbers, we subtract the sum of the first five numbers from the total sum of all numbers:

\[ \text{Sum of remaining 15 numbers} = \text{Sum of 20 numbers} - \text{Sum of first 5 numbers} = 300 - 60 = 240 \]

### Step 4: Calculate the average of the remaining 15 numbers.
Now, we can find the average of the remaining 15 numbers using the sum we just calculated:

\[ \text{Average of remaining 15 numbers} = \frac{\text{Sum of remaining 15 numbers}}{\text{Total remaining numbers}} = \frac{240}{15} = 16 \]

### Final Answer:
The average of the remaining numbers is **16**.

---