If each of the odd digits in the number 5 4 6 3 8 is decreased by 1 and each of the even digits is increased by 1, then which of the following will be the sum of the digits of the new numbers?

Options

A. 25
B. 26
C. 28
D. none of these

Explanation

To solve the problem, we need to modify the digits of the number 54638 according to the given rules and then find the sum of the new digits.

### Step-by-Step Solution:

1. **Identify the digits**: The number given is 54638. The digits are 5, 4, 6, 3, and 8.

2. **Classify the digits**:
- Odd digits: 5, 3
- Even digits: 4, 6, 8

3. **Modify the odd digits**:
- Decrease each odd digit by 1:
- 5 becomes 5 - 1 = 4
- 3 becomes 3 - 1 = 2

4. **Modify the even digits**:
- Increase each even digit by 1:
- 4 becomes 4 + 1 = 5
- 6 becomes 6 + 1 = 7
- 8 becomes 8 + 1 = 9

5. **New digits**: After applying the modifications, we have the new digits:
- From odd digits: 4 (from 5), 2 (from 3)
- From even digits: 5 (from 4), 7 (from 6), 9 (from 8)

So the new digits are 4, 5, 7, 2, and 9.

6. **Calculate the sum of the new digits**:
- Sum = 4 + 5 + 7 + 2 + 9
- Sum = 27

7. **Conclusion**: The sum of the digits of the new numbers is 27.

### Final Answer:
The sum of the digits of the new numbers is **27**.