Study the following information carefully and answer the questions given below.
Eight persons – P, Q, R, S, T, U, V and W sit around a circular table facing the centre, but not necessarily in the same order.
Q sits two places away from S. Two persons sit between S and P who does not sit adjacent to Q. W sits second to the right of P. T and the one who sits opposite to W are immediate neighbours. As many persons sit between Q and W as between T and V. R sits third to the left of V.
What is the position of S with respect to U?
Correct Answer :
Third to the left
Solution :
The correct option is Third to the left.
Let's solve the arrangement step-by-step for the eight persons (P, Q, R, S, T, U, V, and W) sitting around a circular table facing the centre.
Step 1: Understand the positions
Since 8 people are sitting around a circular table facing the centre, opposite positions have 3 people sitting between them on either side.
Step 2: Place S, Q, P, and W
- "Q sits two places away from S" means there is 1 person between Q and S.
- "Two persons sit between S and P who does not sit adjacent to Q."
- "W sits second to the right of P."
Let's number the 8 circular positions clockwise from 1 to 8.
Let P be at position 1.
Since W sits second to the right of P (clockwise), W is at position 3.
Two persons sit between S and P, so S could be at position 4 or position 6.
- If S is at position 4: Q sits two places away from S (1 person between them), so Q could be at position 2 or 6. But P (pos 1) is not adjacent to Q, so Q cannot be at position 2 or 8. Also, P is not adjacent to Q. If Q is at position 6, then Q is 2 places away from S (pos 4). Position 6 is not adjacent to P (pos 1). This is valid.
- If S is at position 6: Q could be at position 4 or 8. But P is at position 1, so Q cannot be at position 8 (adjacent to P). Thus Q would be at position 4. But let's check further constraints.
Let's test S at position 4:
- P is at pos 1.
- W is at pos 3.
- S is at pos 4.
- Q is at pos 6 (1 person between S and Q; Q is not adjacent to P).
Step 3: Determine positions for T, V, R, and U
- The person opposite to W (pos 3) is at position 7.
- "T and the one who sits opposite to W are immediate neighbours."
So T is adjacent to position 7, meaning T can be at position 8 (since pos 6 is occupied by Q).
Let's check: T at position 8.
- "As many persons sit between Q and W as between T and V."
Between Q (pos 6) and W (pos 3), there is 1 person (pos 4 or 5 depending on direction, counting clockwise: 4 and 5 are 2 persons, counter-clockwise: 2 and 1 are 2 persons; exactly 2 persons sit between 3 and 6 on both sides).
Number of persons between Q (6) and W (3) = 2 persons.
Therefore, 2 persons must sit between T (8) and V.
Going counter-clockwise from 8: 7, 6 are 2 persons, so V is at position 5.
- "R sits third to the left of V."
Facing the centre, left of V (pos 5) is clockwise (5 → 6 → 7 → 8).
1st left of V = pos 6
2nd left of V = pos 7
3rd left of V = pos 8
Wait, position 8 is already occupied by T. Going counter-clockwise (right): facing centre, clockwise is left. Let's re-verify directions:
Facing centre:
- Clockwise = Left
- Counter-clockwise = Right
Let's re-check with clockwise = Left:
- W is second to the right of P (counter-clockwise): P at 1, W at 7.
Let's use explicit positions 1 to 8 in clockwise order:
Position 1, Position 2 (Left of 1), Position 3 (Left of 2), ..., Position 8 (Right of 1).
Let P be at position 1.
Right of P (counter-clockwise) is position 8. Second to the right of P is W at position 7.
The person opposite to W (pos 7) is at position 3.
Two persons sit between S and P (pos 1): S can be at position 4 or position 6.
Case A: S is at position 4.
Q is two places away from S (1 person between them): Q can be at pos 2 or pos 6.
Since P (pos 1) is not adjacent to Q, Q cannot be at pos 2. So Q is at position 6.
Now, between Q (6) and W (7), there are 0 persons on one side and 5 persons on the other. But earlier we had:
Case B: S is at position 6.
Q is two places away from S: Q can be at pos 4 or pos 8.
Since P (pos 1) is not adjacent to Q, Q cannot be at pos 8. So Q is at position 4.
Now let's count persons between Q (4) and W (7):
Between pos 4 and pos 7: 2 persons (pos 5, 6) on one side, and 2 persons (pos 1, 2, 3 -> wait, 3 persons: 8, 1, 2, 3? No, 8, 1, 2, 3 is 4 persons).
So there are 2 persons between Q and W (positions 5 and 6).
"As many persons sit between Q and W as between T and V." Thus 2 persons must sit between T and V.
The person opposite to W (pos 7) is position 3.
"T and the one who sits opposite to W are immediate neighbours."
So T is adjacent to position 3, meaning T is at pos 2 or pos 4. Since pos 4 is Q, T is at position 2.
Between T (pos 2) and V, there must be 2 persons.
If V is at pos 7, it's occupied by W. So V must be at position 5 (between pos 2 and pos 5 are positions 3, 4 which is 2 persons).
So V is at position 5.
"R sits third to the left of V."
Left of V (pos 5) is clockwise: 1st left = pos 6, 2nd left = pos 7, 3rd left = position 8.
So R is at position 8.
Now the remaining position for U is position 3.
Final Seating Arrangement (Clockwise from 1 to 8):
1: P
2: T
3: U
4: Q
5: V
6: S
7: W
8: R
Step 4: Find the position of S with respect to U
- U is at position 3.
- S is at position 6.
Counting clockwise (to the left) from U (pos 3):
- 1st to the left of U = Q (pos 4)
- 2nd to the left of U = V (pos 5)
- 3rd to the left of U = S (pos 6)
Therefore, S is Third to the left of U.
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