A, B, C, D, E, F, G and H are sitting in a circle in the same order for lunch at equal distances, Their positions are clockwise. If C is sitting in the east, then what is be the position of G?
West
Solving the Circular Seating Arrangement Puzzle
This question involves a circular seating arrangement where people are placed at equal distances in a clockwise order. We are given the position of one person (C) and need to find the position of another person (G).
There are 8 people (A, B, C, D, E, F, G, H) sitting in a circle at equal distances. Since there are 8 people, the circle is divided into 8 equal sectors. The angle between any two adjacent people is \( \frac{360^\circ}{8} = 45^\circ \).
The standard directions are:
- North (\(0^\circ\) or \(360^\circ\))
- East (\(90^\circ\))
- South (\(180^\circ\))
- West (\(270^\circ\))
The intercardinal directions are:
- North-East (\(45^\circ\))
- South-East (\(135^\circ\))
- South-West (\(225^\circ\))
- North-West (\(315^\circ\))
We are told that C is sitting in the East. In terms of degrees, East corresponds to \(90^\circ\).
The people are sitting in a clockwise order: A, B, C, D, E, F, G, H.
Let's determine the position of each person relative to C, moving clockwise at \(45^\circ\) intervals:
| Person | Position Relative to C (Clockwise) | Angle from North | Direction |
|---|---|---|---|
| C | \(0^\circ\) from self | \(90^\circ\) | East |
| D | \(45^\circ\) Clockwise from C | \(90^\circ + 45^\circ = 135^\circ\) | South-East |
| E | \(45^\circ\) Clockwise from D (\(90^\circ + 2 \times 45^\circ = 180^\circ\)) | \(180^\circ\) | South |
| F | \(45^\circ\) Clockwise from E (\(90^\circ + 3 \times 45^\circ = 225^\circ\)) | \(225^\circ\) | South-West |
| G | \(45^\circ\) Clockwise from F (\(90^\circ + 4 \times 45^\circ = 270^\circ\)) | \(270^\circ\) | West |
Alternatively, we can move counter-clockwise from C. The order counter-clockwise would be C, B, A, H, G, F, E, D.
Moving counter-clockwise at \(45^\circ\) intervals:
| Person | Position Relative to C (Counter-Clockwise) | Angle from North | Direction |
|---|---|---|---|
| C | \(0^\circ\) from self | \(90^\circ\) | East |
| B | \(45^\circ\) Counter-Clockwise from C | \(90^\circ - 45^\circ = 45^\circ\) | North-East |
| A | \(45^\circ\) Counter-Clockwise from B (\(90^\circ - 2 \times 45^\circ = 0^\circ\)) | \(0^\circ\) | North |
| H | \(45^\circ\) Counter-Clockwise from A (\(90^\circ - 3 \times 45^\circ = -45^\circ\) or \(315^\circ\)) | \(315^\circ\) | North-West |
| G | \(45^\circ\) Counter-Clockwise from H (\(90^\circ - 4 \times 45^\circ = -90^\circ\) or \(270^\circ\)) | \(270^\circ\) | West |
Both methods confirm that G is at the \(270^\circ\) position, which corresponds to West.
Final Position of G
Based on the clockwise arrangement starting with C in the East, G is located in the West direction.
Revision Table: Circular Seating and Directions
| Concept | Explanation | Application in Problem |
|---|---|---|
| Circular Arrangement | People or objects arranged in a circle. | 8 people A-H in a circle. |
| Equal Distance | Spacing between adjacent items is constant. | Angle between adjacent people is \(360^\circ / 8 = 45^\circ\). |
| Clockwise Order | Sequence follows the direction of a clock's hands. | A, B, C, ..., H sequence matters for relative positions. |
| Cardinal Directions | North, East, South, West. | C is placed in the East direction. |
| Intercardinal Directions | North-East, South-East, South-West, North-West. | Used for intermediate positions. |
Additional Information on Seating Arrangements and Directions
Seating arrangement questions are common in reasoning sections of competitive exams. They test your ability to understand and follow spatial relationships and logical constraints. When dealing with circular arrangements and directions, it's helpful to visualize the setup or draw a diagram.
- Visualisation: Imagine a compass overlaid on the circle. North is typically at the top, East to the right, South at the bottom, and West to the left.
- Degrees: Relating directions to degrees (North \(0^\circ\), East \(90^\circ\), South \(180^\circ\), West \(270^\circ\)) is crucial, especially when dealing with equal spacing.
- Relative Positions: Phrases like "to the immediate right" or "two places away" are interpreted based on the direction the people are facing (if specified) or relative to the center of the circle in absence of facing direction. In this problem, the clockwise order and equal distance define the relative positions clearly.
- Clockwise vs. Counter-clockwise: Pay close attention to the specified order (clockwise or counter-clockwise) for placing individuals around the circle.
Practice with different numbers of people and varying starting positions will help improve speed and accuracy in solving these types of circular seating arrangement problems.
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