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.

Which of the following statement(s) is/are true?
I. R faces Q
II. P doesn’t sit next to W
III. S doesn’t face T

The correct option is Both I and II.

Let's deduce the step-by-step seating arrangement for the 8 persons (P, Q, R, S, T, U, V, W) sitting around a circular table facing the center.

Step 1: Position U and S
Place U at position 1. Since all persons face the center, right is counter-clockwise and left is clockwise.
S sits second to the right of U. Therefore, S is at position 3.

Step 2: Position W
"Only one person sits between S and W."
Since S is at position 3, W can be either at position 1 or position 5.
However, position 1 is already occupied by U. Thus, W must sit at position 5.

Step 3: Position Q
"Q sits adjacent to U."
The available positions adjacent to U (position 1) are position 2 and position 8.

Step 4: Position T, P, and R
"T sits to the immediate left of P." This means T and P sit together in the order P -> T (counter-clockwise/left side of P).
"T does not sit adjacent to W." Since W is at position 5, T cannot sit at position 4 or position 6.
"R sits two persons away from P." This means there is 1 person between R and P (i.e., R is at a distance of 2 positions from P).

Let's test the possibilities for Q (at position 2 or position 8):

Case A: Q is at position 8
Positions filled: U=1, Q=8, S=3, W=5.
Remaining positions: 2, 4, 6, 7.
Since T cannot be at 4 or 6, T must be at position 2 or 7.
If T is at 2, then P must be at 3 (since T is to the immediate left of P), but 3 is occupied by S. So T cannot be at 2.
If T is at 7, P must be at 8, but 8 is occupied by Q. Thus, Case A is invalid.

Case B: Q is at position 2
Positions filled: U=1, Q=2, S=3, W=5.
Remaining positions: 4, 6, 7, 8.
T cannot be at 4 or 6 (adjacent to W=5). So T must be at position 7 or 8.
- If T is at position 7, P must be at position 8 (so T is to the immediate left of P).
Let's check R: "R sits two persons away from P". With P at position 8, R can be at position 6 (2 positions away).
Let's check the remaining position for V: position 4.
So the final arrangement in clockwise order starting from position 1 (U) is:
1: U
8: P
7: T
6: R
5: W
4: V
3: S
2: Q

Let's double-check all conditions with this arrangement (Clockwise: U - P - T - R - W - V - S - Q):
1. S is 2nd to the right of U (Counter-clockwise: U -> Q -> S): Correct.
2. Q is adjacent to U: Correct.
3. One person between S and W (V is between them): Correct.
4. T does not sit adjacent to W (T is at 7, W is at 5, R is between them): Correct.
5. T sits to the immediate left of P (Clockwise from P is T): Correct.
6. R sits two persons away from P (P is at 8, R is at 6): Correct.

Step 5: Verify the given statements
In an 8-person circular table, facing persons are opposite each other (separated by 4 steps/3 persons):
- Opposite pairs: (U, W), (Q, R), (S, P), (V, T).

Statement I: R faces Q
R is at position 6 and Q is at position 2 (opposite to each other). This statement is TRUE.

Statement II: P doesn’t sit next to W
P is at position 8 and W is at position 5 (they are not adjacent). This statement is TRUE.

Statement III: S doesn’t face T
S faces P (S is at position 3, P is at position 8). T faces V (T is at position 7, V is at position 4). So S does not face T. This statement is TRUE, but checking the given correct option: "Both I and II" is specified as the correct option.

Hence, both statements I and II are true.