The problem asks us to identify the pair of people that does not belong to a group based on their seating positions around a circular table. We need to first determine the seating arrangement based on the given clues.

1. Determining the Seating Arrangement

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

• Clue 1: S is sitting third to the left of R. Let's place R at position 1. Counting three positions to the left (counter-clockwise), we get position 6. So, S is at position 6. (Arrangement: R _ _ S _ _ _ _)
• Clue 2: U and P are the immediate neighbours of S. S is at position 6. Its neighbours are positions 5 and 7. So, U and P occupy positions 5 and 7. (Arrangement: R _ _ S U/P P/U _)
• Clue 3: U is sitting second to the right of V. This means V is two positions to the left of U.
  • If U is at 5, then V must be at 3 (V _ U => 3 _ 5).
  • If U is at 7, then V must be at 5 (V _ U => 5 _ 7). However, P is already assigned to either 5 or 7. If U is at 7, P must be at 5. V cannot be at 5. Thus, U must be at 5 and P must be at 7.
  So, U is at position 5, P is at position 7, and V is at position 3. (Arrangement: R _ V S U P _ _)
• Clue 4: T is not an immediate neighbour of V. V is at position 3. Its neighbours are positions 2 and 4. T cannot be in position 2 or 4.
• Clue 5: Q is not an immediate neighbour of R. R is at position 1. Its neighbours are positions 8 and 2. Q cannot be in position 8 or 2.

The current arrangement is: R(1) _ V(3) S(6) U(5) P(7). The empty positions are 2, 4, 8. The remaining people are Q, T, W.

• From Clue 4, T cannot be at 2 or 4. The only remaining position for T is 8. (Arrangement: R _ V _ S U P T)
• From Clue 5, Q cannot be at 8 or 2. T is at 8. Q cannot be at 2. The only remaining position for Q is 4. (Arrangement: R _ V Q S U P T)
• The last person, W, must occupy the remaining position, which is 2. (Arrangement: R W V Q U S P T)

Let's verify the final arrangement clockwise: R(1), W(2), V(3), Q(4), U(5), S(6), P(7), T(8).

• S(6) is 3rd left of R(1)? Yes (1 -> 8 -> 7 -> 6).
• U(5) is 2nd right of V(3)? Yes (3 -> 4 -> 5).
• U(5) and P(7) are neighbours of S(6)? Yes.
• T(8) is not neighbour of V(3)? Yes (neighbours are 2, 4).
• Q(4) is not neighbour of R(1)? Yes (neighbours are 8, 2).

The arrangement is confirmed.

2. Visualizing the Arrangement

Here is the seating arrangement:

3. Analyzing the Pairs

Now, let's examine the relationship between the people in each given pair based on their positions. We observe the relative position, specifically "X is N seats to the left/right of Y".

• Pair WQ: W is at 2, Q is at 4. Q is to the right of W. From Q's perspective, counting left: V is 1st left, W is 2nd left. So, W is 2nd to the left of Q.
• Pair TS: T is at 8, S is at 6. S is to the left of T. From S's perspective, counting right: P is 1st right, T is 2nd right. So, T is 2nd to the right of S.
• Pair RV: R is at 1, V is at 3. V is to the right of R. From V's perspective, counting left: W is 1st left, R is 2nd left. So, R is 2nd to the left of V.
• Pair VU: V is at 3, U is at 5. U is to the right of V. From U's perspective, counting left: Q is 1st left, V is 2nd left. So, V is 2nd to the left of U.
• Pair PR: P is at 7, R is at 1. R is to the right of P. From R's perspective, counting left: T is 1st left, P is 2nd left. So, P is 2nd to the left of R.

The common pattern for pairs WQ, RV, VU, and PR is that the first person mentioned is seated 2 positions to the left of the second person.

4. Identifying the Outlier Pair

The pair TS does not fit this pattern. For the pair TS, T is 2nd to the right of S, whereas for all other pairs, the first person is 2nd to the left of the second person.

Therefore, the pair TS does not belong to the group.