Trains at fixed intervals — find the announcement time A train to Lucknow departs every 2 hours 30 minutes from New Delhi. An announcement says: “The previous train left 40 minutes ago and the next train will leave at 18:00 hrs.” At what time was this announcement made?

Introduction / Context:
Departures occur every 2 h 30 min. Knowing the time of the next departure allows us to infer the previous departure and thus “now,” given the “40 minutes ago” statement.

Given Data / Assumptions:

• Next departure: 18:00.
• Interval: 2 h 30 min.
• Previous train left 40 minutes before the announcement.

Step-by-Step Solution:
Previous scheduled departure = 18:00 − 2:30 = 15:30.If the previous train “left 40 minutes ago,” the current time = 15:30 + 0:40 = 16:10.

Verification / Alternative check:
Time from announcement (16:10) to next departure (18:00) is 1 h 50 min. Adding to the 40 min since the previous yields the full 2 h 30 min interval.

Why Other Options Are Wrong:
15:30 is the time of the previous departure, not the announcement; 16:00 and 17:10 do not satisfy the interval partition (40 min elapsed + remaining to 18:00 = 2:30).

Common Pitfalls:
Confusing “previous departure time” with “announcement time.”

Final Answer:
16.10 hrs