If all the persons are arranged in alphabetical order from senior most to junior most designation, then the position of how many persons remains unchanged?

Study the following information carefully and answer the questions given below:

Nine persons - P, Q, R, S, T, U, V, W and X are working in the company at different designations such as MD, CEO, CFO, CRO, COO, GM, DM, HR and TL but not necessarily in the same order. The designations are given in decreasing order, such that MD is the senior-most designation and TL is the junior-most designation.

X is four persons junior to Q who is senior to CRO. The number of persons senior to Q is one less than the number of persons junior to S. Only three persons are designated between S and T. P is two persons junior to T. The number of persons designated between P and U is one less than the number of persons designated between U and V who is senior to X. W is senior to R who is not TL.

To solve the puzzle, we first list the designations in decreasing order of seniority as specified in the problem:
1. MD (Senior-most)
2. CEO
3. CFO
4. CRO
5. COO
6. GM
7. DM
8. HR
9. TL (Junior-most)

Let us determine the positions of the nine persons (P, Q, R, S, T, U, V, W, and X) step-by-step:

Step 1: Analyze Q and X
X is four designations junior to Q. This means if Q is at position $q$, X is at position:

$q+4$

Step 2: Analyze the relation between Q and S
The number of persons senior to Q is one less than the number of persons junior to S.
If Q is at position 1: Persons senior to Q = 0. Thus, persons junior to S = 1, placing S at position 8 (HR).
If Q is at position 2: Persons senior to Q = 1. Thus, persons junior to S = 2, placing S at position 7 (DM).
If Q is at position 3: Persons senior to Q = 2. Thus, persons junior to S = 3, placing S at position 6 (GM).

Step 3: Analyze S and T
Only three persons are designated between S and T.
If S is at position 8: T must be at position 4. Since Q is at 1, X must be at 5. P is two designations junior to T, so P is at 6. The remaining positions are 2, 3, 7, and 9.
If S is at position 7: T must be at position 3. Since Q is at 2, X must be at 6. P is two designations junior to T, so P is at 5. The remaining positions are 1, 4, 8, and 9.
If S is at position 6: T must be at position 2. Since Q is at 3, X must be at 7. P is two designations junior to T, so P is at 4. The remaining positions are 1, 5, 8, and 9.

Step 4: Place U, V, W, and R
Let's test the second scenario (Q = 2, S = 7, T = 3, P = 5, X = 6, with positions 1, 4, 8, 9 remaining):
V is senior to X (6), so V must be at position 4 (since 1, 8, 9 are the other free spots and V must be senior to 6).
Now we analyze the condition: "The number of persons designated between P and U is one less than the number of persons designated between U and V".
If we place U at position 9:
The number of persons between P (5) and U (9) is 3 (positions 6, 7, 8).
The number of persons between U (9) and V (4) is 4 (positions 5, 6, 7, 8).
Since 3 is indeed one less than 4, this condition is perfectly satisfied.
Now, the remaining positions are 1 and 8. The remaining persons are W and R. Since W is senior to R, W is placed at position 1 (MD) and R is placed at position 8 (HR). Since R is not TL (which is position 9), this configuration is valid.

Hence, the final arrangement of the persons from senior-most to junior-most is:
1. MD: W
2. CEO: Q
3. CFO: T
4. CRO: V
5. COO: P
6. GM: X
7. DM: S
8. HR: R
9. TL: U

Step 5: Compare with Alphabetical Order
Now, we arrange all the nine persons in alphabetical order from senior-most to junior-most:
1. MD: P (Originally W)
2. CEO: Q (Originally Q)
3. CFO: R (Originally T)
4. CRO: S (Originally V)
5. COO: T (Originally P)
6. GM: U (Originally X)
7. DM: V (Originally S)
8. HR: W (Originally R)
9. TL: X (Originally U)

Comparing the two lists, only Q remains at the same position (CEO).

Therefore, the position of only one person remains unchanged.