Average of 12 numbers is 15. If a number 41 is also included, then what will be the average of these 13 numbers ?

Options

A. 16
B. 18
C. 19
D. 17

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the sum of the original 12 numbers
Given that the average of 12 numbers is 15, we can find the sum of these numbers using the formula for average:

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

Let the sum of the 12 numbers be \( S \). Therefore, we have:

\[ 15 = \frac{S}{12} \]

To find \( S \), we multiply both sides by 12:

\[ S = 15 \times 12 \]

Calculating this gives:

\[ S = 180 \]

### Step 2: Add the new number to the sum
Now, we include the number 41 to the sum we just calculated:

\[ \text{New Sum} = S + 41 = 180 + 41 = 221 \]

### Step 3: Calculate the new average
Now that we have the new sum, we can find the average of the 13 numbers. The new average \( A \) can be calculated as follows:

\[ A = \frac{\text{New Sum}}{\text{Total numbers}} = \frac{221}{13} \]

### Step 4: Perform the division
Now, we will divide 221 by 13:

\[ 221 \div 13 = 17 \]

Thus, the new average of the 13 numbers is:

\[ \text{New Average} = 17 \]

### Final Answer
The average of these 13 numbers is **17**.

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