Direction for the following 3 (three) items: Consider the given information and answer the three items (76-78) that follow.

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 Answer: Option A (A)

To determine which station need not be passed through when travelling from station H to station C (with the route between G and C closed), let us map out all the available connections (passages) between the stations based on the given information.

1. Understanding the Passages:

• One-way passages:

C ⇒ A
E ⇒ G
B ⇒ F
D ⇒ H
G ⇒ C
E ⇒ C
H ⇒ G

• Two-way passages:

A ⇔ E
G ⇔ B
F ⇔ D
E ⇔ D

2. Analyzing the Path from H to C:

We need to travel starting from station H and reach station C.

• From H, the available outgoing routes are:
- One-way passage: H ⇒ G

• From G, normally we could take G ⇒ C. However, the problem specifies that the route between G and C is closed. Thus, from G we must use the two-way passage: G ⇔ B (i.e., G ⇒ B).

• From B, the only outgoing passage is the one-way passage: B ⇒ F.

• From F, the available passage is the two-way passage: F ⇔ D (i.e., F ⇒ D).

• From D, we can use the two-way passage: D ⇔ E (i.e., D ⇒ E).

• From E, we have a direct one-way passage to C: E ⇒ C.

3. Trace of the Complete Route:

$\text{H}\to \text{G}\to \text{B}\to \text{F}\to \text{D}\to \text{E}\to \text{C}$

4. Conclusion:

The stations passed through on this route are G, B, F, D, and E. Station A is not on this path and therefore need not be passed through while travelling from H to C.