Consider the following A, B, C, D, E, F, G and H are standing in a row facing North.
B is not a neighbour of G.
F is to the immediate right of G and is a neighbour of E.
G is not at the extreme end.
A is sixth to the left of E.
H is sixth to the right of C.
Which one of the following is correct in respect of the above?

Correct Option (3)

The final arrangement of the eight individuals, A, B, C, D, E, F, G, and H, in a row facing North, is determined by systematically applying the given conditions:

• "A is sixth to the left of E" implies a sequence of seven positions with A at the leftmost and E at the sixth position to its right (A _ _ _ _ _ E).
• "H is sixth to the right of C" implies a sequence of seven positions with C at the leftmost and H at the sixth position to its right (C _ _ _ _ _ H).
• "F is to the immediate right of G and is a neighbour of E" establishes the contiguous block GFE.
• "G is not at the extreme end," meaning there is at least one person to G's left.
• "B is not a neighbour of G."

Considering a row of 8 positions (P1 to P8):

1. From "A is sixth to the left of E," A can be at P1 and E at P7, or A at P2 and E at P8.
2. From "H is sixth to the right of C," C can be at P1 and H at P7, or C at P2 and H at P8.
3. If A is at P1 and E is at P7, the arrangement starts as A _ _ _ _ _ E _.
4. The block GFE must align with E at P7. This places G at P5 and F at P6. The arrangement becomes A _ _ _ G F E _.
5. The remaining positions are P2, P3, P4, P8. The remaining individuals are B, C, D, H.
6. To satisfy "H is sixth to the right of C" with C and H among the remaining, C must be at P2 and H at P8. This forms A C _ _ G F E H.
7. The remaining individuals B and D must occupy P3 and P4.
8. If D is at P3 and B at P4 (A C D B G F E H), B would be a neighbour of G, violating the condition "B is not a neighbour of G."
9. Therefore, B must be at P3 and D at P4. This yields the unique arrangement: A C B D G F E H.

In this arrangement, D is at the fourth position from the left (P4) and G is at the fifth position from the left (P5). Thus, G is to the immediate right of D, making option (3) correct.

Incorrect Options:

• Option (1): C is to the immediate left of A.

  In the derived arrangement (A C B D G F E H), A is at P1 and C is at P2. This indicates that C is to the immediate right of A, not to its immediate left.

• Option (2): D is the immediate neighbour of B and F.

  In the derived arrangement (A C B D G F E H), D is at P4. Its immediate neighbours are B (at P3) and G (at P5). D is not a neighbour of F (which is at P6).

• Option (4): A and E are at the extreme ends.

  In the derived arrangement (A C B D G F E H), A is at P1, which is an extreme end. However, E is at P7, and H is at P8. Therefore, E is not at an extreme end.