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 option is One.

Step 1: Understand the Seating Arrangement Rules

There are eight persons: P, Q, R, S, T, U, V, and W sitting around a circular table facing the center.

Since everyone faces the center of the table:

• Clockwise movement corresponds to moving towards the Left.

• Anti-clockwise (counter-clockwise) movement corresponds to moving towards the Right.

Let us number eight positions 1 through 8 in a clockwise direction around the table.

Step 2: Step-by-Step Position Allocation

1. Place U and S:

Let U be seated at Position 1.

S sits second to the right (anti-clockwise) of U.

Moving two positions anti-clockwise from Position 1 brings us to Position 7.

Therefore, S is at Position 7.

2. Place W:

Only one person sits between S and W. This means W can be 2 positions away from S in either direction (Position 5 or Position 1).

Since Position 1 is already occupied by U, W must be placed at Position 5.

3. Place Q:

Q sits adjacent to U (Position 1). So Q must sit at either Position 2 or Position 8.

4. Place P and T:

T sits to the immediate left (clockwise) of P. So if P is at Position $k$, then T is at Position $k+1$.

We are given that T does not sit adjacent to W. Since W is at Position 5, T cannot be at Position 4 or Position 6.

If Q is at Position 8, the available positions for P and T are Position 2 and Position 3 respectively.

Thus, P is at Position 2 and T is at Position 3.

5. Place R and V:

R sits two persons (places) away from P (Position 2). Moving two places clockwise gives Position 4.

Thus, R is at Position 4.

The remaining person, V, takes the last open position, which is Position 6.

Final Original Seating Order (Clockwise from Position 1 to 8):

• Position 1: U

• Position 2: P

• Position 3: T

• Position 4: R

• Position 5: W

• Position 6: V

• Position 7: S

• Position 8: Q

Step 3: Rearranging in Alphabetical Order

Now, let us arrange all persons in alphabetical order starting from P in an anti-clockwise direction (moving from Position 2 to 1, 8, 7, 6, 5, 4, 3):

• Position 2: P (Starting reference point)

• Position 1: Q (Original: U)

• Position 8: R (Original: Q)

• Position 7: S (Original: S) ⇒ Unchanged

• Position 6: T (Original: V)

• Position 5: U (Original: W)

• Position 4: V (Original: R)

• Position 3: W (Original: T)

Comparing the original and new positions (excluding P at Position 2), only S at Position 7 retains its original seat.

Hence, exactly One person remains unchanged in their position.