Solving the Circular Seating Arrangement Puzzle

This question involves a circular seating arrangement puzzle. We have 7 people: Radha, Rekha, Rakhi, Ragini, Rashmi, Reema, and Renu, all sitting around a circle and facing the center. To solve this, we will use the given clues to deduce their exact positions.

Understanding the Clues

Let's break down the information provided:

• (i) Seven people are in a circle facing the center.
• (ii) Reema is not an immediate neighbour of Rashmi.
• (iii) Radha is to the immediate right of Ragini. (Clockwise direction relative to Ragini's position)
• (iv) Rekha is second to the left of Reema. (Counter-clockwise direction relative to Reema's position, with one person between them)
• (v) Radha is third to the left of Renu. (Counter-clockwise direction relative to Renu's position, with two people between them)

Step-by-Step Deduction of the Arrangement

Let's start placing people based on the most direct clues (iii) and (v), which link Radha to two other people. Since it's a circle of 7 people, positions are relative.

From clue (iii), "Radha is to the immediate right of Ragini". If we place Ragini, Radha is in the next position clockwise.

From clue (v), "Radha is third to the left of Renu". Moving counter-clockwise from Renu, the first person is at Renu's immediate left, the second person is next, and the third person is Radha. This means there are two people between Renu and Radha when moving from Renu towards Radha in a counter-clockwise direction.

Let's combine (iii) and (v). We have a segment like this (clockwise order):

... Ragini > Radha ...

And a segment from (v) (counter-clockwise order):

... Radha <- Person 2 <- Person 1 <- Renu ...

Combining these for a 7-person circle:

If we start with Ragini at position 1, then Radha is at position 2 (immediate right).

Positions (clockwise): 1, 2, 3, 4, 5, 6, 7

Person: Ragini(1), Radha(2), _, _, _, _, _

Radha (at position 2) is 3rd to the left (counter-clockwise) of Renu. Starting from Renu, moving left: Renu -> 1st left -> 2nd left -> 3rd left (Radha). So, if Radha is at 2, we move 3 steps clockwise from Radha to find Renu: 2 -> 3 -> 4 -> 5. Renu is at position 5.

Current partial arrangement:

Pos: 1, 2, 3, 4, 5, 6, 7

Person: Ragini, Radha, _, _, Renu, _, _

Empty spots are 3, 4, 6, 7.

Remaining people: Rakhi, Rashmi, Reema, Rekha.

Now let's use clue (iv): "Rekha is second to the left of Reema". This means there is one person between Reema and Rekha (when moving counter-clockwise from Reema).

We need to place Reema and Rekha in the empty spots (3, 4, 6, 7) such that Rekha is two positions counter-clockwise from Reema.

Let's test possible positions for Reema and see if Rekha can be placed:

• If Reema is at 3: 2nd left is 1 (Ragini - occupied). Not possible.
• If Reema is at 4: 2nd left is 2 (Radha - occupied). Not possible.
• If Reema is at 6: 2nd left is 4. This works, as 4 is empty. Reema at 6, Rekha at 4.
• If Reema is at 7: 2nd left is 5 (Renu - occupied). Not possible.

So, Reema must be at position 6, and Rekha must be at position 4.

Current arrangement:

Pos: 1, 2, 3, 4, 5, 6, 7

Person: Ragini, Radha, _, Rekha, Renu, Reema, _

Empty spots are 3 and 7.

Remaining people: Rakhi and Rashmi.

Finally, use clue (ii): "Reema is not an immediate neighbour of Rashmi". Reema is at position 6. Her immediate neighbours are at positions 5 (Renu) and 7. This means Rashmi cannot be at position 7.

Since Rashmi cannot be at 7, and the empty spots are 3 and 7, Rashmi must be at position 3.

The last remaining person is Rakhi, who must be at the last empty spot, position 7.

Final Arrangement

The final arrangement (clockwise) is:

Pos: 1, 2, 3, 4, 5, 6, 7

Person: Ragini, Radha, Rashmi, Rekha, Renu, Reema, Rakhi

Let's verify all clues with this arrangement:

• (i) Yes, 7 people in a circle.
• (ii) Reema (6) neighbours are Renu (5) and Rakhi (7). Rashmi (3) neighbours are Radha (2) and Rekha (4). Reema is not next to Rashmi. Yes.
• (iii) Radha (2) is immediate right of Ragini (1). Yes (1 -> 2 clockwise).
• (iv) Rekha (4) is second left of Reema (6). From 6 (counter-clockwise): 6 -> 5 (Renu) -> 4 (Rekha). Yes.
• (v) Radha (2) is third left of Renu (5). From 5 (counter-clockwise): 5 -> 4 (Rekha) -> 3 (Rashmi) -> 2 (Radha). Yes.

All conditions are met. The arrangement is:

In a circular order, moving clockwise: Ragini, Radha, Rashmi, Rekha, Renu, Reema, Rakhi.

Answering the Question

The question asks which group has the first person sitting between the other two. This means the first person is an immediate neighbour of both the second and the third person in the group.

Let's check each option based on our final arrangement:

• A. Reema-Rashmi-Radha: Is Reema between Rashmi and Radha? Reema's neighbours are Renu and Rakhi. Rashmi's neighbours are Radha and Rekha. Radha's neighbours are Ragini and Rashmi. Reema is not between Rashmi and Radha.
• B. Rakhi-Ragini-Reema: Is Rakhi between Ragini and Reema? Rakhi's neighbours are Reema and Ragini (from the arrangement: ...Reema(6) -> Rakhi(7) -> Ragini(1)...). Yes, Rakhi is an immediate neighbour of both Ragini and Reema.
• C. Renu-Rekha-Ragini: Is Renu between Rekha and Ragini? Renu's neighbours are Rekha and Reema. Ragini's neighbours are Rakhi and Radha. Renu is not between Rekha and Ragini.
• D. Renu-Rekha-Rakhi: Is Renu between Rekha and Rakhi? Renu's neighbours are Rekha and Reema. Rakhi's neighbours are Reema and Ragini. Renu is not between Rekha and Rakhi.

Based on the analysis, only option B fits the condition.

Revision Table: Key Concepts

Additional Information: Seating Arrangement Strategies

Seating arrangement questions are common in logic and reasoning sections. Here are some tips for solving them effectively:

• Visualize: Draw a diagram (circle, line, square, etc.) corresponding to the arrangement.
• Start with Definite Information: Look for clues that fix the position of one or two individuals relative to each other or a fixed point (if any). Clues like "A is to the immediate right of B" or "C is at one end" are good starting points.
• Connect Clues: Find clues that link individuals who have already been placed or link new individuals to the existing partial arrangement.
• Handle Negative Information: Clues like "X is NOT a neighbour of Y" are useful for eliminating possibilities later in the process, often after a partial arrangement is formed.
• Consider All Possibilities (if needed): If a clue has multiple potential placements, explore each possibility. Sometimes one path will lead to a contradiction with another clue, allowing you to eliminate it.
• Verify the Final Arrangement: Once you have a complete arrangement, read through all the original clues again and check if your arrangement satisfies every single condition.
• Answer the Specific Question: After finding the arrangement, carefully read what the question is asking and use your diagram to find the answer.