A daily train is to be introduced between station A and station B starting from each 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?

Correct Option (3)

To maintain a daily shuttle service between Station A and Station B, a train must depart from each station at 6 AM every day. The journey duration for each train is 42 hours.

• On Day 1, two trains are required to initiate the service: one departing from Station A towards B, and another departing from Station B towards A.
• As the journey takes 42 hours, these initial two trains will still be en route at 6 AM on Day 2.
• To ensure a daily departure, two additional trains must depart at 6 AM on Day 2: one from Station A and one from Station B.
• Therefore, at 6 AM on Day 2, there are four trains actively involved in the service: the two trains that departed on Day 1 (still in transit) and the two new trains departing on Day 2.
• The trains that departed on Day 1 will complete their journey at 12 AM (midnight) on Day 3 (6 AM Day 1 + 42 hours).
• This operational model demonstrates that a minimum of four trains are necessary to sustain continuous daily departures from both stations.

Incorrect Options:

Option 1 (2 trains): This number is insufficient. If only two trains were available, the trains departing on Day 1 would not complete their 42-hour journey and return to their origin station until Day 3, thereby failing to provide a daily service on Day 2.

Option 2 (3 trains): This number is also insufficient. Three trains cannot maintain simultaneous daily departures from both stations given the 42-hour journey time, as it would leave one station without a departing train on a given day or require an impossible turnaround time.

Option 4 (7 trains): This number is excessive. The calculation based on the daily departure requirement and journey duration indicates that four trains are sufficient to maintain the shuttle service.