If the number $624739854$ is transformed such that **1 is added to all even digits** and **1 is subtracted from all odd digits**, then what is the sum of the digits which is **fifth from the left end** and **fourth from the right end** in the transformed number?

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**Solution:**

1. The original number is:
   $$6 \, 2 \, 4 \, 7 \, 3 \, 9 \, 8 \, 5 \, 4$$

2. Identify the digits and their positions:
   - 1st digit (leftmost): 6
   - 2nd digit: 2
   - 3rd digit: 4
   - 4th digit: 7
   - 5th digit: 3
   - 6th digit: 9
   - 7th digit: 8
   - 8th digit: 5
   - 9th digit (rightmost): 4

3. Apply the transformation rules:
   - Add 1 to all even digits
   - Subtract 1 from all odd digits

Let's transform each digit:

| Digit | Even/Odd | Transformation | Result |
   |-------|----------|----------------|--------|
   | 6     | Even     | 6 + 1          | 7      |
   | 2     | Even     | 2 + 1          | 3      |
   | 4     | Even     | 4 + 1          | 5      |
   | 7     | Odd      | 7 - 1          | 6      |
   | 3     | Odd      | 3 - 1          | 2      |
   | 9     | Odd      | 9 - 1          | 8      |
   | 8     | Even     | 8 + 1          | 9      |
   | 5     | Odd      | 5 - 1          | 4      |
   | 4     | Even     | 4 + 1          | 5      |

4. The transformed number is:
   $$7 \, 3 \, 5 \, 6 \, 2 \, 8 \, 9 \, 4 \, 5$$

5. Identify the digits:
   - Fifth from the left end: 5th digit = 2
   - Fourth from the right end: 4th digit from right = 6th digit from left = 8

6. Sum these two digits:
   $$2 + 8 = 10$$

**Answer:** 10

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