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?
Answer & explanation
Answer: (c) 4
A train leaving at 6 AM arrives 42 hours later, at midnight, and can start back only at the next 6 AM — so each one-way trip uses 2 days and a round trip 4 days. With a departure needed every day, 4 trains keep the shuttle going.
- Leaving A at 6 AM on day 1, a train reaches B 42 hours later — midnight at the end of day 2.
- It starts back from B at 6 AM on day 3 and reaches A at midnight at the end of day 4.
- It leaves A again at 6 AM on day 5: one full cycle takes 4 days.
- A train must leave A every day, so 4 trains are needed (trains 1–4 leave A on days 1–4; train 1 is back for day 5).
- Check: the same 4 trains also give a daily 6 AM departure from B, each leaving B two days after leaving A.
Remember · For a shuttle, find one train's full cycle, waiting included; trains needed = cycle in days × daily departures from one end.
Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·