A daily train is to be introduced between station A and station B starting from each end at 6 AM and the journey is to be completed in 42 hours. What is the number of trains needed in order to maintain the shuttle service ?

The correct option is 4.

To find the number of trains required to maintain a daily shuttle service between station A and station B, we can analyze the schedule and turnaround time for the trains.

Let us break down the timeline step-by-step:
1. A train starts from Station A at 6 AM on Day 1 (let us call this Train 1).
2. The journey takes 42 hours. 42 hours is equal to 24 hours (1 full day) + 18 hours.
3. Therefore, Train 1 arriving at Station B will reach at:
6 AM (Day 1) + 24 hours = 6 AM (Day 2)
6 AM (Day 2) + 18 hours = 12 AM (Midnight of Day 2 / start of Day 3).
So, Train 1 completes its journey at Station B at 12 AM (Midnight) between Day 2 and Day 3.

4. Since the departure from Station B back to Station A must happen at 6 AM, this train (Train 1) can only depart from Station B at 6 AM on Day 3.
5. The return journey also takes 42 hours, reaching Station A at 12 AM (Midnight) between Day 4 and Day 5. This train can start its next cycle from Station A at 6 AM on Day 5.

Thus, the total turnaround time for one train to start from Station A, go to Station B, and be ready to start from Station A again is:
From 6 AM on Day 1 to 6 AM on Day 5, which is exactly 4 days (or 96 hours).

Since a train is dispatched from Station A every single day at 6 AM, and a train takes 4 days to return to Station A and be ready for its next trip, we need 4 separate trains to cover the departures from Station A on Day 1, Day 2, Day 3, and Day 4.
By Day 5, the train from Day 1 (Train 1) is back and ready to cover the Day 5 departure. Similarly, the train from Day 2 covers Day 6, and so on.

Thus, the minimum number of trains needed to maintain the shuttle service is:
$$\text{Number of trains}=4$$