Question

Akash, Bidhan, Chandan, Dinesh, Esha, and Farooq are seated around a circular table facing the center. 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.
Howmanypersons are seated to the left of Akash and to the right of Esha?

• A. 2
• B. 4
• C. 3
• D. 5

Hint:

In circular seating arrangements, fix one person first and build the rest using the constraints. Always verify all conditions once an arrangement is made.

Answer 1

The Correct Option is C

Step 1: Fix positions in a circular arrangement.
Label the six positions around the circular table clockwise as:
Position 1, Position 2, Position 3, Position 4, Position 5, Position 6. Step 2: Use condition 1: Chandan is third to the right of Farooq.
Assume Farooq is at Position 1. Then Chandan is at Position 4 (third to the right). Step 3: Use condition 2: Bidhan is second to the right of Chandan.
Chandan is at Position 4 → Bidhan is at Position 6 (second to the right). So far: Farooq = Position 1
Chandan = Position 4
Bidhan = Position 6
Step 4: Apply condition 3: Dinesh is not sitting next to Chandan.
Chandan is at Position 4 → neighbors are Positions 3 and 5 $$ \Rightarrow \text{Dinesh cannot be at Position 3 or 5} $$ Step 5: Apply condition 4: Akash is not sitting next to Bidhan.
Bidhan is at Position 6 → neighbors are Positions 5 and 1 $$ \Rightarrow \text{Akash cannot be at Position 5 or 1} $$ Step 6: Assign remaining people to positions:
Remaining positions: 2, 3, 5
Remaining people: Akash, Dinesh, Esha
From above:
Dinesh \( \neq 3 \) or \( 5 \) \( \Rightarrow \) Dinesh = 2
Akash \( \neq 1 \) or \( 5 \) \( \Rightarrow \) Akash = 3 Esha = 5
Final arrangement:
\includegraphics[width=0.4\linewidth]{19.png}
Step 7: Determine how many persons are seated to the left of Akash and to the right of Esha.
Akash is at Position 3
Esha is at Position 5
To find the people between Esha (Position 5) and Akash (Position 3), we count the positions moving clockwise from Esha to Akash:
From Esha (Position 5) to Akash (Position 3):
Position 6: Bidhan
Position 1: Farooq
Position 2: Dinesh
Thus, there are 3 people between Esha and Akash. Conclusion: $$ \boxed{3} $$