Question

Five people -- Akash, Bidhan, Chandan, Dinesh, and Esha -- are sitting around a circular table. The following conditions are given:
1. Chandan is third to the right of Farooq.
2. Bidhan is second to the right of Chandan.
3. Dinesh is not sitting next to Chandan.
4. Akash is not sitting next to Bidhan
Which pair is sitting next to each other?

• A. Farooq- Chandan
• B. Chandan- Akash
• C. Dinesh- Esha
• D. Bidhan- Akash

Hint:

For circular arrangement problems, fix one person's position first and build the rest of the arrangement step-by-step using the constraints. Always verify all conditions once an arrangement is made.

Answer 1

The Correct Option is B

Step 1: Set up positions in a circular arrangement.
Label the five positions around the table as:
Position 1, Position 2, Position 3, Position 4, Position 5 (in clockwise order). Step 2: Use condition 1: Chandan is third to the right of Farooq. \[ \text{If Farooq is at Position 1} \Rightarrow \text{Chandan is at Position 4}. \] Step 3: Use condition 2: Bidhan is second to the right of Chandan. \[ \text{Chandan at Position 4} \Rightarrow \text{Bidhan is at Position 1}. \] Step 4: Assign Farooq, Chandan, and Bidhan:
Position 1: Bidhan
Position 4: Chandan
So, Farooq must be at Position 5 (since Chandan is third to the right of Farooq).
Step 5: Use condition 3: Dinesh is not sitting next to Chandan.
Chandan is at Position 4 $\Rightarrow$ Neighbors are Positions 3 and 5 \[ \Rightarrow \text{Dinesh cannot be at Position 3 or 5} \] Step 6: Use condition 4: Akash is not sitting next to Bidhan.
Bidhan is at Position 1 $\Rightarrow$ Neighbors are Positions 5 and 2 \[ \Rightarrow \text{Akash cannot be at Position 5 or 2} \] Step 7: Fill remaining positions:
Remaining positions: 2, 3
Remaining people: Akash, Dinesh, Esha
From above:
Dinesh $\neq$ 3 or 5 $\Rightarrow$ Dinesh = 2
Akash $\neq$ 1 or 2 $\Rightarrow$ Akash = 3
Esha = 5
\includegraphics[width=0.4\linewidth]{16.png}
Step 8: Check adjacency:
Farooq (5) and Chandan (4): Adjacent
Chandan (4) and Akash (3): Adjacent
Dinesh (2) and Esha (5): Not adjacent
Bidhan (1) and Akash (3): Not adjacent
Conclusion: Only pair that is adjacent is: $$ \boxed{\text{Chandan - Akash}} $$