Eight persons – P, Q, R, S, T, U, V and W sit around a circular table facing the center but not necessarily in the same order.
S sits second to the right of U. Q sits adjacent to U. Only one person sits between S and W. T does not sit adjacent to W. T sits to the immediate left of P. R sits two persons away from P.

If all persons sit in alphabetical order from P in anti-clockwise direction, then how many persons remain unchanged in their position (excluding P)?

The correct answer is One.

Let's solve the arrangement step-by-step based on the given information for eight persons (P, Q, R, S, T, U, V, W) sitting around a circular table facing the center (clockwise direction is to the left of a person, anti-clockwise direction is to the right of a person):

1. Positions of U and S:
Let us place U at position 1. Since S sits second to the right of U (anti-clockwise direction from U), S is at position 3.

2. Positions of W:
Only one person sits between S and W. This gives two possibilities for W:
- Case A: W is at position 1 (occupied by U, so invalid).
- Case B: W is at position 5.

3. Positions of Q:
Q sits adjacent to U. So Q can be at position 2 or position 8.

4. Positions of T, P, R:
- T sits to the immediate left of P (which means P is immediately to the right / anti-clockwise of T).
- T does not sit adjacent to W (so T cannot be at positions 4 or 6).
- R sits two persons away from P (meaning there is 1 person between R and P).

Let's test Q at position 8:
Remaining open positions are 2, 4, 6, 7.
Since T cannot be at 4 or 6, T can be at 2 or 7.
- If T is at 7, then P (to the immediate right of T) is at 8, but 8 is occupied by Q.
- If T is at 2, then P is at 3, but 3 is occupied by S.
Therefore, Q cannot be at position 8.

Thus, Q must be at position 2.
Now available positions for T, P, R, V are 4, 6, 7, 8.
Since T cannot be at 4 or 6, T must be at 7.
Since T is at position 7, P sits to the immediate right of T, so P is at position 8.
R sits two persons away from P (1 person between P and R), so R can be at position 6.
The remaining person V must be at position 4.

Initial Seating Arrangement (in anti-clockwise order starting from position 1):

Position 1: U
Position 2: Q
Position 3: S
Position 4: V
Position 5: W
Position 6: R
Position 7: T
Position 8: P

Rearrangement according to the question:
All persons sit in alphabetical order starting from P in the anti-clockwise direction (positions 8, 1, 2, 3, 4, 5, 6, 7):

Position 8: P (given: P)
Position 1: Q (original: U)
Position 2: R (original: Q)
Position 3: S (original: S) – Unchanged
Position 4: T (original: V)
Position 5: U (original: W)
Position 6: V (original: R)
Position 7: W (original: T)

Comparing the new positions with the original positions (excluding P):
Only S at Position 3 remains in the same position.

Therefore, exactly One person remains unchanged in their position.