Eight railway stations A, B, C, D, E, F, G and H are connected either by two-way passages or one-way passages. One-way passages are from C to A, E to G, B to F, D to H, G to C, E to C and H to G. Two-way passages are between A and E, G and B, F and D, and E and D.
If the route between G and C is closed, which one of the following stations need not be passed through while travelling from H to C?

Correct Option (A)

To determine which station need not be passed through while travelling from H to C, given that the route between G and C is closed, all possible valid routes must be identified. The specified passages are:

• One-way: C→A, E→G, B→F, D→H, E→C, H→G.
• Two-way: A↔E, G↔B, F↔D, E↔D.

With the G→C route closed, the only possible path from H to C is constructed as follows:

1. The journey begins at H. The only outgoing one-way passage from H is H→G.
2. From G, the two-way passage G↔B allows travel to B (G→B).
3. From B, the one-way passage B→F allows travel to F.
4. From F, the two-way passage F↔D allows travel to D (F→D).
5. From D, the two-way passage E↔D allows travel to E (D→E).
6. From E, the one-way passage E→C allows travel to C.

Thus, the complete and unique path from H to C is H → G → B → F → D → E → C. In this path, stations G, B, F, D, and E are traversed. Station A is not included in this sequence. Therefore, A is the station that need not be passed through.

Incorrect Options:

• E: Station E is a mandatory component of the identified path (H → G → B → F → D → E → C). It provides the only available connection to C (E→C) after the G→C route closure, making its passage essential.
• D: Station D is an indispensable part of the path (H → G → B → F → D → E → C). It serves as a critical link between F and E (F↔D and D↔E), which is necessary to reach E and subsequently C.
• B: Station B is a crucial intermediary in the path (H → G → B → F → D → E → C). It connects G to F (G↔B and B→F), thereby facilitating the progression of the journey towards C.