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
P, M, D, A, F, H, R and B are sitting around a circle facing at the centre. R is fourth to the right of A, who is third to the right of P. M is second to the left of H, who is second to the left of P. D is third to the right of B. Which of the following pairs are immediate neighbors of B?
Six people, K, L, M, N, O and P, are sitting on the ground in a hexagonal shape but not necessarily in the same order. K is not sitting next to L or M. N is not sitting next to M or O. L is the neighbour of M. P is in the middle of M and N. What is the correct order of seating positions of the people in clockwise direction?
Six friends, G, H I, J, K and L, are sitting around a circular table, facing towards the centre of the table. H is sitting third to the left of G. L and I are not neighbours of H. K is sitting to the immediate right of I. Who is sitting to the immediate left of L?
Eight friends A, B, C, D, E, F, G and are sitting around a circular table facing each other for a lunch. A is opposite F and third to the right of B. G is between F and D. H is to the left of D. E is between C and A. Who is sitting third to the right of A?
Six friends are sitting at equal distances from each other in a circle and facing the centre of the circle. Diraj is between Pramod and Parthiv. Priyanshu is between Mukund and Laya. Pramod and Mukund are opposite to each other. Laya is to the immediate left of Pramod. Who is sitting to the immediate left of Parthiv?
