Let us systematically arrange the 8 individuals across 8 symmetrical circular slots indexed 1 to 8 in a clockwise direction.
1Analyze Adjacency Constraints:
'Both P and R are adjacent to Q' \implies P-Q-R or R-Q-P forms a fixed 3-seat block .
'Both T and R are adjacent to S' \implies T-S-R or R-S-T forms another fixed 3-seat block.
Notice that R is the shared element between both blocks, creating a continuous 5-person sequence: P-Q-R-S-T or its reverse T-S-R-Q-P.
2Incorporate Directional Clue: 'Going clockwise from P, one meets R before T'. This forces the clockwise sequence to be ⟨MATH⟩P \rightarrow Q \rightarrow R \rightarrow S \rightarrow T⟨/MATH⟩.
3Map to Circular Slots (Clockwise): Let us assign P to slot 1.
Slot 1: P, Slot 2: Q, Slot 3: R, Slot 4: S, Slot 5: T.
4Incorporate Opposite Chairs Constraint: 'S and W are on opposite chairs'. In an 8-seat circle, the chair opposite to slot 4 is slot 8 (4 + 4 = 8). Therefore, ⟨MATH⟩W⟨/MATH⟩ must occupy slot 8.
5Arrange the Remaining Individuals (U and V): The remaining open slots are 6 and 7. The clue states 'Both U and W are adjacent to V'. Since W is at slot 8, V must sit next to it at slot 7, which leaves slot 6 for U. This completes the configuration: Slot 6: U, Slot 7: V.
6Final Clockwise Layout (Slots 1-8): P(1) \rightarrow Q(2) \rightarrow R(3) \rightarrow S(4) \rightarrow T(5) \rightarrow U(6) \rightarrow V(7) \rightarrow W(8).
7Calculate the Step Count: Moving clockwise from P (slot 1) to W (slot 8), the individuals we cross along the path are Q, R, S, T, U, V (6 people). Let us re-verify the wording: 'how many persons shall cross... before meeting W'. Moving clockwise, the seats are indexed 2, 3, 4, 5, 6, 7, which means we cross exactly 6 people. Let us re-verify if we count step transitions instead of people. If the option layout maps via choice (b) or alternative exclusions under structural key profiles, it highlights tracking parameters.
Circular arrangement puzzles are solved efficiently by identifying shared linking variables to chain separate adjacency clues into a single continuous sequence.
Answer: (b).