Eight persons P, Q, R, S, T, U, V and W sit around a round table in eight different seats placed with equal distance between any two consecutive seats. Both P and R are adjacent to Q. Both T and R are adjacent to S. Both U and W are adjacent to V. S and W are on opposite chairs. If while going in the clockwise direction around the table from P, one meets R before T, then how many persons shall Q cross while moving in the clockwise direction around the table before meeting W?

The correct option is (a) - 5.

[as per provisional answerkey]

Step-by-step Trace

We need to arrange 8 persons (P, Q, R, S, T, U, V, W) around a circular table based on the given constraints:

• Constraint 1: P and R are adjacent to Q. This means the sequence is P-Q-R or R-Q-P.
• Constraint 2: T and R are adjacent to S. This means the sequence is T-S-R or R-S-T.
• Constraint 3: U and W are adjacent to V. This means the sequence is U-V-W or W-V-U.
• Constraint 4: S and W are on opposite chairs. In an 8-seat table, "opposite" means there are 3 seats between them in either direction.
• Constraint 5: Moving clockwise from P, one meets R before T.

Building the arrangement:
1. From Constraints 1 and 2, we see that R is the common link. The sequence must be P - Q - R - S - T (or the reverse).
2. Let's place S at position 1. Since S and W are opposite, W must be at position 5.
3. From Constraint 2, R and T are adjacent to S. So R and T occupy positions 2 and 8.
4. From Constraint 1, P and R are adjacent to Q. This means Q must be between P and R. If R is at position 2, Q is at 3 and P is at 4. If R is at 8, Q is at 7 and P is at 6.
5. Now apply Constraint 5: Clockwise from P, R comes before T.
- If we use the sequence P(4), Q(3), R(2), S(1), T(8): Clockwise from P(4) to R(2) goes through 5, 6, 7, 8, 1. This is a long way. Let's check the other way.
- If we use the sequence P(6), Q(7), R(8), S(1), T(2): Clockwise from P(6), we hit R(8) then S(1) then T(2). This satisfies "R before T".
6. Now place the remaining group (U, V, W). We know W is at position 5. From Constraint 3, U and W are adjacent to V. Since position 6 is taken by P, V must be at position 4 and U must be at position 3.
7. Final Clockwise Arrangement: S(1) - T(2) - U(3) - V(4) - W(5) - P(6) - Q(7) - R(8).

Answering the question:
Moving clockwise from Q (position 7) to W (position 5):
Q(7) -> R(8) -> S(1) -> T(2) -> U(3) -> V(4) -> W(5).
The persons crossed are: R, S, T, U, V. Total = 5 persons.

Why the other options are incorrect

• Option (b) - 4: This count would be correct if we skipped one person or if the table had only 7 seats; however, in an 8-seat arrangement with this specific logic, 5 people stand between Q and W clockwise.
• Option (c) - 2: This would be the count if we moved anti-clockwise from Q to W (crossing only P and V), but the question specifically demands the clockwise direction.
• Option (d) - 1: This would imply Q and W are almost adjacent, which contradicts the fixed positions of S, R, and P between them.

Key Concept

Circular arrangement logic requiring the integration of adjacency constraints, opposite-seating rules, and directional relative positioning.