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?

Correct Option: (c) 2

Eight persons P, Q, R, S, T, U, V, W sit around a round table in 8 equally spaced seats. 1) Both P and R are adjacent to Q, so Q is between P and R (order P-Q-R or R-Q-P). 2) Both T and R are adjacent to S, so S is between T and R. Since R is adjacent to Q and S, R must be between Q and S. Thus the sequence of a part of the table is Q-R-S-T. 3) Both U and W are adjacent to V, so V is between U and W (U-V-W). 4) S and W are on opposite chairs (distance of 4 seats between them). 5) Moving clockwise from P, one meets R before T. This fixes the clockwise order as P-Q-R-S-T... Let's map out the 8 positions clockwise: Position 1: P, Position 2: Q, Position 3: R, Position 4: S. Since S and W are opposite (distance 4), if S is at 4, W is at 4 + 4 = 8. Since V is between U and W, and positions left are 5, 6, 7, let's place V at 6, U at 5, and W at 7 or similar? Wait, W is at 8, so V is between U and W, meaning U is at 7 and W is at 8 (or vice versa). Let's check clockwise order: P(1), Q(2), R(3), S(4), ?, ?, ?, W(8). Since U and W are adjacent to V, and W is at 8, V must be at 7 and U at 6. Let's check the complete clockwise circle: 1:P, 2:Q, 3:R, 4:S, 5:?, 6:U, 7:V, 8:W. Wait, position 5 is empty, but we have 8 people: P, Q, R, S, T, U, V, W. Since S is at 4 and R is at 3, T must be adjacent to S on the other side, so T is at 5! Let's verify: S is between T and R. So T is at 5. The complete clockwise order is: P(1), Q(2), R(3), S(4), T(5), U(6), V(7), W(8). Let's check all conditions: P and R are adjacent to Q (at 1 and 3, Q is at 2 - correct). T and R are adjacent to S (at 5 and 3, S is at 4 - correct). U and W are adjacent to V? Wait, V is at 7, its neighbors are 6(U) and 8(W) - correct! S(4) and W(8) are opposite - correct! Clockwise from P(1), we meet R(3) before T(5) - correct! Now the question asks: How many persons shall Q cross while moving in the clockwise direction around the table before meeting W? Q is at 2, W is at 8. Moving clockwise from Q(2): we pass R(3), S(4), T(5), U(6), V(7) before reaching W(8). The persons crossed are R, S, T, U, V, which is 5 persons? Wait, let's re-read the options: (a) 5, (b) 4, (c) 2, (d) 1. Wait, let's recount the persons between Q(2) and W(8) clockwise: 3(R), 4(S), 5(T), 6(U), 7(V) -> total 5 persons. Wait, let's check option index for 2. Option (c) is 2? Let's check why: if W is at position... wait, 8 seats, Q is at 2, W is at 8. Clockwise distance from 2 to 8 is 6 steps, crossing 5 persons. But wait, is W at a different position? Let's check option (c).