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 ?

(a) 2
(b) 3
(c) 4 ✓ UPSC's answer
(d) 7

Why the answer is (c)

• The total journey time for a single train from one station to the other is 42 hours.

• Since the service is a shuttle, a train must return to its starting point to begin the next cycle, making the total cycle time 42 hours (outbound) + 42 hours (inbound) = 84 hours.

• Trains are scheduled to depart from each end every 24 hours (daily at 6 AM).

• To maintain continuous service, the number of trains required is the total cycle time divided by the departure interval: 84 hours / 24 hours = 3.5.

• Since a fraction of a train cannot be used, we must round up to the next whole number to ensure no gap in service.

• Therefore, 4 trains are needed to cover the 84-hour cycle with 24-hour intervals.

Why the other options are wrong

(a) 2: 2 trains would only cover a 48-hour cycle, leaving a 36-hour gap in service.
(b) 3: 3 trains would cover a 72-hour cycle, which is less than the required 84-hour cycle, causing a 12-hour gap.
(d) 7: 7 trains are excessive; only 4 are required to cover the 84-hour cycle with 24-hour intervals.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.