A, B, C, D, E, F, G and H are sitting in a circle in the same order, at equal distances. Their positions are clockwise. If C is sitting in the East, then what will be the position of E?
South
Understanding Circular Seating Arrangement and Directions
This question involves a circular seating arrangement and understanding cardinal and intercardinal directions. We are given that eight people are sitting in a circle in a specific order and one person's position relative to the directions. We need to find the position of another person.
Analyzing the Seating Arrangement
- There are 8 people: A, B, C, D, E, F, G, H.
- They are sitting in a circle.
- They are in the same order clockwise: A, B, C, D, E, F, G, H.
- They are at equal distances from each other.
Since they are at equal distances in a circle, the angle between any two adjacent people is uniform. A full circle is $360^\circ$. With 8 people, the angle between adjacent people is:
$$ \text{Angle between adjacent people} = \frac{360^\circ}{\text{Number of people}} = \frac{360^\circ}{8} = 45^\circ $$
So, each person is $45^\circ$ clockwise from the person before them in the sequence A, B, C, ...
Determining Positions Based on C's Location
We are told that C is sitting in the East direction.
We need to find the position of E. Let's trace the positions clockwise starting from C:
- C is in the East.
- The next person clockwise is D. D is $45^\circ$ clockwise from C. $45^\circ$ clockwise from East is South-East. So, D is in the South-East.
- The next person clockwise is E. E is $45^\circ$ clockwise from D. E is $45^\circ$ clockwise from South-East. $45^\circ$ from South-East towards clockwise brings us to South. So, E is in the South.
We can also think of this in terms of number of positions. E is two positions clockwise away from C (C → D → E). Each position is a $45^\circ$ turn clockwise. So, E is $2 \times 45^\circ = 90^\circ$ clockwise from C.
If C is in the East, $90^\circ$ clockwise from East is South.
Let's visualize or list the positions starting from C in the East:
- C: East ($0^\circ$ relative to East)
- D: $45^\circ$ clockwise from East (South-East)
- E: $90^\circ$ clockwise from East (South)
- F: $135^\circ$ clockwise from East (South-West)
- G: $180^\circ$ clockwise from East (West)
- H: $225^\circ$ clockwise from East (North-West)
- A: $270^\circ$ clockwise from East (North)
- B: $315^\circ$ clockwise from East (North-East)
This confirms that if C is in the East, E is in the South.
Conclusion
Based on the clockwise arrangement and C being in the East, the position of E is in the South.
| Person | Positions Clockwise from C | Angle Clockwise from East | Direction |
|---|---|---|---|
| C | 0 | $0^\circ$ | East |
| D | 1 | $1 \times 45^\circ = 45^\circ$ | South-East |
| E | 2 | $2 \times 45^\circ = 90^\circ$ | South |
Revision Table: Key Concepts
| Concept | Description |
|---|---|
| Circular Arrangement | Objects or people placed in a circle. |
| Equal Distance | Points are spaced uniformly around the circle, implying equal angles between them from the center. |
| Clockwise Order | Following the sequence in the direction of a clock's hands. |
| Cardinal Directions | North, South, East, West, spaced $90^\circ$ apart. |
| Intercardinal Directions | North-East, South-East, South-West, North-West, halfway between cardinal directions ($45^\circ$ apart). |
Additional Information: Directions and Angles
Understanding the relationship between directions and angles is crucial for solving circular arrangement problems involving directions.
- A full circle is $360^\circ$.
- The main cardinal directions (N, E, S, W) are $90^\circ$ apart.
- Starting from East ($0^\circ$ or $360^\circ$), moving clockwise:
- East: $0^\circ$
- South-East: $45^\circ$
- South: $90^\circ$
- South-West: $135^\circ$
- West: $180^\circ$
- North-West: $225^\circ$
- North: $270^\circ$
- North-East: $315^\circ$
- Moving counter-clockwise from East:
- East: $0^\circ$
- North-East: $315^\circ$ (or $-45^\circ$)
- North: $270^\circ$ (or $-90^\circ$)
- etc.
In this problem, since the people are equally spaced and in clockwise order, each step to the next person in the sequence A, B, C, ... corresponds to moving $45^\circ$ clockwise around the circle from the previous person's position.
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?
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?
