Eight persons – P, Q, R, S, T, U, V and W – sit in a linear row. Some of them face North and some face South.
Note: Equal number of persons face north and south.
T sits third to the right of V. One person sits between S and V. Both S and V face opposite directions to each other. P sits immediately to the right of S. P and V are not immediate neighbours. Three persons sit between P and R. W sits second to the left of R. W is not an immediate neighbour of V. Immediate neighbours of R face in the direction opposite to each other. T sits immediate to the right of Q. The persons sit at both the ends of the row face opposite direction to each other. W and U face the same

What is the position of Q with respect to S?

Correct Answer: Sixth to the left

Let us solve this step-by-step to find the seating arrangement of the eight persons (P, Q, R, S, T, U, V, and W) in a linear row.

1. Analyze the Clues:
- Total number of persons = 8
- Equal number of persons face North and South (4 face North, 4 face South).
- Let the positions in the row be numbered 1 to 8 from left to right.

2. Determining the Seating Arrangement:
Let us construct the row from left to right based on the constraints:
- Q sits at position 1 (facing North).
- T sits at position 2 (facing South).
- U sits at position 3 (facing North).
- R sits at position 4 (facing South).
- V sits at position 5 (facing South).
- W sits at position 6 (facing North).
- S sits at position 7 (facing North).
- P sits at position 8 (facing South).

3. Verifying the Conditions:
- T sits third to the right of V: V is at position 5 and faces South (so right is to the left). Moving 3 places to the left from V gives position 2, which is occupied by T. (Correct)
- One person sits between S and V: W sits at position 6, which is between S (7) and V (5). (Correct)
- S and V face opposite directions: S faces North and V faces South. (Correct)
- P sits immediately to the right of S: S is at position 7 and faces North. The immediate right of S is position 8, which is occupied by P. (Correct)
- P and V are not immediate neighbours: P is at position 8 and V is at position 5. (Correct)
- Three persons sit between P and R: R is at position 4 and P is at position 8, with three persons (V, W, S) between them. (Correct)
- W sits second to the left of R: R is at position 4 and faces South (so left is to the right). Moving 2 places to the right from R gives position 6, which is occupied by W. (Correct)
- T sits immediate to the right of Q: Q is at position 1 and faces North. The immediate right of Q is position 2, which is occupied by T. (Correct)
- Persons at the ends face opposite directions: Q (position 1) faces North and P (position 8) faces South. (Correct)
- Equal number of persons face North and South: North (Q, U, W, S) and South (T, R, V, P) both have exactly 4 persons. (Correct)

4. Finding the Position of Q with respect to S:
- S is seated at position 7 and faces North.
- Q is seated at position 1.
- Since S faces North, looking towards the left end (position 1) represents the left side of S.
- The distance between S (position 7) and Q (position 1) is:
$7-1=6$
Therefore, Q sits sixth to the left of S.