Eight friends, P, Q, R, S, T, U, V and W, are sitting in the same order anticlockwise around a circular table at equal distance between them, with all centre of the table. If Q is sitting in the south-east, then in which direction is W sitting?
South-west
Understanding the Circular Seating Arrangement
This question involves a circular seating arrangement where eight friends, P, Q, R, S, T, U, V, and W, are sitting around a circular table. They are positioned at equal distances from each other and are all facing the center of the table. The order in which they are sitting is given as P, Q, R, S, T, U, V, and W in an anticlockwise direction.
We are given a specific condition: Q is sitting in the South-East direction.
Our goal is to determine the direction in which W is sitting.
Mapping Directions in the Circular Arrangement
A circular table with 8 positions equally spaced means that the angle between any two adjacent friends is \( \frac{360^\circ}{8} = 45^\circ \). The eight standard directions (North, North-East, East, South-East, South, South-West, West, North-West) are also \(45^\circ\) apart.
We are told that the friends are in the order P, Q, R, S, T, U, V, W in an anticlockwise direction. This means if you start at P and move anticlockwise around the circle, you will encounter Q, then R, then S, and so on, until W, before returning to P.
Let's use the given information that Q is in the South-East (SE) direction to fix the positions.
Since the order P, Q, R, ... W is anticlockwise:
- Q is anticlockwise to P. This means P is clockwise to Q. The angle between neighbours is \(45^\circ\). So, P is \(45^\circ\) clockwise from Q. If Q is in South-East, which is between South and East, \(45^\circ\) clockwise from South-East is South. So, P is in the South direction.
- R is anticlockwise to Q. This means R is \(45^\circ\) anticlockwise from Q. If Q is in South-East, \(45^\circ\) anticlockwise from South-East is East. So, R is in the East direction.
We can continue this pattern, moving \(45^\circ\) anticlockwise for each subsequent friend in the given order (P, Q, R, S, T, U, V, W).
Let's list the directions starting from P based on this:
- P: South (\(45^\circ\) clockwise from Q)
- Q: South-East (Given)
- R: East (\(45^\circ\) anticlockwise from Q)
- S: North-East (\(45^\circ\) anticlockwise from R)
- T: North (\(45^\circ\) anticlockwise from S)
- U: North-West (\(45^\circ\) anticlockwise from T)
- V: West (\(45^\circ\) anticlockwise from U)
- W: South-West (\(45^\circ\) anticlockwise from V)
Confirming the Circular Arrangement and Directions
Let's verify the sequence and directions in a table format, moving anticlockwise:
| Friend | Direction | Relative Position (Anticlockwise) |
|---|---|---|
| P | South | Start |
| Q | South-East | 45° anticlockwise from P |
| R | East | 45° anticlockwise from Q |
| S | North-East | 45° anticlockwise from R |
| T | North | 45° anticlockwise from S |
| U | North-West | 45° anticlockwise from T |
| V | West | 45° anticlockwise from U |
| W | South-West | 45° anticlockwise from V |
According to this mapping, where Q is in South-East and the order P, Q, R, ..., W is followed anticlockwise, W is found to be sitting in the South-West direction.
Final Answer Deduction
Based on the given information and the step-by-step deduction of each friend's position relative to Q (who is in South-East), we determined the direction for each person in the sequence P, Q, R, S, T, U, V, W as they appear anticlockwise around the table. By following this pattern, W is located 7 positions away from Q in the anticlockwise direction (or 1 position away in the clockwise direction, which is the same relative positioning just viewed differently), ultimately placing W in the South-West direction.
Revision Table: Seating Arrangement Basics
| Concept | Description |
|---|---|
| Circular Arrangement | People are seated around a circle (table, etc.). |
| Facing Center | When facing the center, 'left' is clockwise and 'right' is anticlockwise (or vice versa, depending on your starting point, but relative positions between people are fixed). Here, we use directions, which are absolute. |
| Anticlockwise Order | The sequence of people encountered when moving against the direction of clock hands. |
| Equal Distance | Implies positions are separated by equal angles (360° / number of people). For 8 people, it's 45°. |
| Direction Mapping | Relating seating positions to standard geographical directions (N, S, E, W, NE, SE, SW, NW). |
Additional Information: Directions and Angles
Understanding the relationship between directions and angles is crucial for solving such circular arrangement problems involving directions.
- North is typically considered 0° or 360°.
- Moving clockwise: East is 90°, South is 180°, West is 270°.
- The intermediate directions are at 45° angles: North-East (45°), South-East (135°), South-West (225°), North-West (315°).
- In this problem with 8 positions, each position is exactly 45° away from its neighbors.
- Moving anticlockwise means decreasing the angle (unless crossing the 0/360 boundary). Moving clockwise means increasing the angle.
When Q is in South-East (135°), and friends are ordered P, Q, R... anticlockwise, it means R is at \(135^\circ - 45^\circ = 90^\circ\) (East), S is at \(90^\circ - 45^\circ = 45^\circ\) (North-East), and so on. Similarly, P, being before Q in the anticlockwise sequence, is at \(135^\circ + 45^\circ = 180^\circ\) (South). This confirms the sequence and directions derived earlier.
Important Questions from Circular Arrangement
Seven friends, Subhi, Prince, Ketan, Vishal, Mahima, Krish and Naitik, are sitting around a circular table with their backs towards the centre. Subhi is sitting to the immediate right of Prince. Naitik and Krish are not sitting to the immediate left or right of Vishal. Vishal is sitting third to the left of Prince. Mahima is sitting to the immediate right of Vishal. Who is sitting third to the right of Prince?
Raghav, Manpreet, Sunaina, Prakrit, Vedika and Arwa are sitting around a circular table facing the centre. Raghav is second to the left of Prakrit. Manpreet is to the immediate left of Sunaina. Arwa is second to the right of Vedika. There are an equal number of persons between Raghav and Manpreet from both the ends. Who is sitting third to the left of Sunanina?
Five friends, Vishnu, Chirag, Raina, Kavya and Surbhi, are sitting around a circular table, facing the center. Vishnu is to the immediate right of Kavya. Chirag is third to the left of Kavya. Surbhi is not adjacent to Chirag. Who is second to the left of Kavya?
Six friends, David, Bhanu, Minto, Krita, John and Nisan, are sitting in a circle with their backs towards the centre. David and Minto are sitting to the immediate left and right of Bhanu, respectively. John is not sitting to the immediate left of David. Nisan is sitting third to the right of Bhanu. Who is sitting second to the left of Bhanu?
Six children, G, H, I, J, K, and L, are sitting around a circular table facing towards the centre. J and K are sitting to the immediate left and right of G, respectively. L is sitting to the immediate left of J, but not to the immediate right of H. Who is sitting to the immediate right of K?
