Circular Seating Arrangement Analysis

This problem involves a circular seating arrangement puzzle with eight individuals: Rohan, Raunak, Sushma, Sandip, Reshma, Sahil, Ruhi, and Sristi. All are seated around a circle and are facing the centre. We need to determine the position of Reshma with respect to Sristi based on the given clues.

Key Constraints and Clues

• Constraint 1: Rohan is second to the right of Reshma.
• Constraint 2: Reshma is the neighbour of Sushma and Sahil.
• Constraint 3: Sandip is not the neighbour of Rohan.
• Constraint 4: Sahil is the neighbour of Ruhi.
• Constraint 5: Raunak is not between Sandip and Sristi.
• Constraint 6: Sristi is not between Ruhi and Sandip.

Step-by-Step Solution Building

Let's systematically place the individuals around the circle, numbering the positions 1 through 8 in a clockwise direction for clarity, starting from Position 1 at the top and proceeding clockwise.

Initial Placements Based on Strong Clues

1. From Constraint 1, "Rohan is second to the right of Reshma," let's place Reshma at Position 1. Moving two positions to the right (clockwise), Rohan must be at Position 3.
   • Position 1: Reshma
   • Position 2: (Empty)
   • Position 3: Rohan
2. From Constraint 2, "Reshma is the neighbour of Sushma and Sahil," it means Sushma and Sahil must occupy Position 2 and Position 8 (the positions immediately adjacent to Reshma at Position 1).
   • Position 8: Sushma/Sahil
   • Position 1: Reshma
   • Position 2: Sushma/Sahil
   • Position 3: Rohan
3. Now, consider Constraint 4, "Sahil is the neighbour of Ruhi."
   • If Sahil were at Position 2, his neighbours would be Reshma (P1) and Rohan (P3). Since Reshma and Rohan are distinct individuals, Ruhi cannot be Sahil's neighbour in this scenario.
   • Therefore, Sahil must be at Position 8.
   • If Sahil is at Position 8, then Sushma must be at Position 2 (to satisfy Constraint 2).
   • For Sahil (P8) to be a neighbour of Ruhi, and Reshma (P1) already being one of Sahil's neighbours, Ruhi must be at Position 7.

Current Seating Arrangement (Partial)

The remaining people are Sandip, Raunak, and Sristi, who must be placed in the remaining open positions: P4, P5, and P6.

Placing Remaining Individuals Using Further Constraints

4. From Constraint 3, "Sandip is not the neighbour of Rohan."
   • Rohan is at P3. His immediate neighbours are P2 (Sushma) and P4.
   • Therefore, Sandip cannot be at P4.
   • This means Sandip must be at either P5 or P6.

Case Analysis: Placing Sandip

We will consider two cases for Sandip's position:

Case A: Sandip is at P5

If Sandip is at P5, then Raunak and Sristi must occupy P4 and P6.

Let's check sub-cases for Raunak and Sristi:

1. **Subcase A.1: Sristi at P4, Raunak at P6**
   • Arrangement: Reshma(P1), Sushma(P2), Rohan(P3), Sristi(P4), Sandip(P5), Raunak(P6), Ruhi(P7), Sahil(P8).
   • Check Constraint 5: "Raunak is not between Sandip and Sristi."
     • The sequence in the circle is …Sristi(P4) –> Sandip(P5) –> Raunak(P6)….
     • Here, Sandip is between Sristi and Raunak. Raunak is clearly not between Sandip and Sristi. This condition holds true.
   • Check Constraint 6: "Sristi is not between Ruhi and Sandip."
     • Sristi (P4) is a neighbour of Sandip (P5).
     • However, Sristi (P4) is not a neighbour of Ruhi (P7). Therefore, Sristi cannot be "between" Ruhi and Sandip. This condition also holds true.
   • This arrangement (Subcase A.1) satisfies all constraints. Let's find the position of Reshma with respect to Sristi for this arrangement:
     • Reshma is at P1, Sristi is at P4.
     • Counting clockwise from Sristi (P4): P5 (Sandip - 1st), P6 (Raunak - 2nd), P7 (Ruhi - 3rd), P8 (Sahil - 4th), P1 (Reshma - 5th).
     • So, Reshma is Fifth to the right of Sristi. This position is not among the given options.

Case B: Sandip is at P6

If Sandip is at P6, then Raunak and Sristi must occupy P4 and P5.

Let's check sub-cases for Raunak and Sristi:

1. **Subcase B.1: Sristi at P4, Raunak at P5**
   • Arrangement: Reshma(P1), Sushma(P2), Rohan(P3), Sristi(P4), Raunak(P5), Sandip(P6), Ruhi(P7), Sahil(P8).
   • Check Constraint 5: "Raunak is not between Sandip and Sristi."
     • The sequence in the circle is …Sristi(P4) –> Raunak(P5) –> Sandip(P6)….
     • Here, Raunak (P5) IS between Sristi (P4) and Sandip (P6), as he is an immediate neighbour to both.
     • This violates Constraint 5. So, this subcase is invalid.
2. **Subcase B.2: Sristi at P5, Raunak at P4**
   • Arrangement: Reshma(P1), Sushma(P2), Rohan(P3), Raunak(P4), Sristi(P5), Sandip(P6), Ruhi(P7), Sahil(P8).
   • Check Constraint 5: "Raunak is not between Sandip and Sristi."
     • The sequence in the circle is …Raunak(P4) –> Sristi(P5) –> Sandip(P6)….
     • Here, Sristi is between Raunak and Sandip. Raunak is clearly not between Sandip and Sristi. This condition holds true.
   • Check Constraint 6: "Sristi is not between Ruhi and Sandip."
     • Sristi (P5) is a neighbour of Sandip (P6).
     • However, Sristi (P5) is not a neighbour of Ruhi (P7). Therefore, Sristi cannot be "between" Ruhi and Sandip. This condition also holds true.
   • This arrangement (Subcase B.2) satisfies all constraints. Let's find the position of Reshma with respect to Sristi for this arrangement:
     • Reshma is at P1, Sristi is at P5.
     • Counting clockwise from Sristi (P5): P6 (Sandip - 1st), P7 (Ruhi - 2nd), P8 (Sahil - 3rd), P1 (Reshma - 4th).
     • So, Reshma is Fourth to the right of Sristi. This position matches one of the given options.

Final Seating Arrangement

Based on our comprehensive analysis, the only arrangement that satisfies all given conditions and provides an answer matching the options is:

Determining Reshma's Position Relative to Sristi

In the final valid seating arrangement:

• Sristi is at Position P5.
• Reshma is at Position P1.

To determine the position of Reshma with respect to Sristi, we count positions clockwise (to the right) from Sristi:

• 1st to the right of Sristi (P5) is Sandip (P6).
• 2nd to the right of Sristi (P5) is Ruhi (P7).
• 3rd to the right of Sristi (P5) is Sahil (P8).
• 4th to the right of Sristi (P5) is Reshma (P1).

Therefore, Reshma is Fourth to the right of Sristi.