If the arithmetic mean of 10 numbers is 35 and each number is incresed by 2, find the mean of the new set of numbers .
A .28
B. 34
C.40
D. 37

Options

A. C
B. A
C. B
D. D

Answer

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

1. **Understand the given information**: We know that the arithmetic mean of 10 numbers is 35.

2. **Calculate the total of the original numbers**:
- The formula for the arithmetic mean is:
\[ \text{Mean} = \frac{\text{Sum of numbers}}{\text{Total numbers}} \]
- Rearranging this, we find the sum of the numbers:
\[ \text{Sum of numbers} = \text{Mean} \times \text{Total numbers} = 35 \times 10 = 350 \]

3. **Determine the effect of increasing each number by 2**:
- If each of the 10 numbers is increased by 2, the total increase in the sum will be:
\[ \text{Total increase} = 2 \times 10 = 20 \]

4. **Calculate the new total**:
- The new sum of the numbers after increasing each by 2 will be:
\[ \text{New sum} = \text{Original sum} + \text{Total increase} = 350 + 20 = 370 \]

5. **Find the new mean**:
- The new mean can be calculated using the new sum:
\[ \text{New Mean} = \frac{\text{New sum}}{\text{Total numbers}} = \frac{370}{10} = 37 \]

6. **Conclusion**: The mean of the new set of numbers is 37.

### Final Answer:
The mean of the new set of numbers is **37** (Option D).