The average of 26 numbers is 37. One more number is added and the new average becomes 41. What is that new number?

Options

A. 140
B. 145
C. 146
D. 147

Answer

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

### Step 1: Calculate the sum of the first 26 numbers
The average of the first 26 numbers is given as 37. We can use the formula for average:

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

From this, we can express the sum of the first 26 numbers (let's call it \( S_1 \)) as:

\[ S_1 = \text{Average} \times \text{Total numbers} = 37 \times 26 \]

Calculating this gives:

\[ S_1 = 37 \times 26 = 962 \]

### Step 2: Calculate the sum of the 27 numbers with the new average
When one more number (let's call it \( y \)) is added, the new average becomes 41. Now we have 27 numbers. We can express the sum of these 27 numbers (let's call it \( S_2 \)) as:

\[ S_2 = \text{New Average} \times \text{Total numbers} = 41 \times 27 \]

Calculating this gives:

\[ S_2 = 41 \times 27 = 1107 \]

### Step 3: Find the new number
The new number \( y \) can be found by subtracting the sum of the first 26 numbers from the sum of the 27 numbers:

\[ y = S_2 - S_1 = 1107 - 962 \]

Calculating this gives:

\[ y = 1107 - 962 = 145 \]

### Conclusion
The new number added is \( 145 \).

---