A train for Fatehpur leaves Agra station every 2 hours 30 minutes. An announcement is made that the previous train left 37 minutes ago and that the next train will arrive at 17:00 hours. At what time was this announcement made?

Introduction / Context:
This is a time schedule and interval problem frequently seen in aptitude tests. Trains are assumed to leave at fixed regular intervals, and we are given information about when the next train is due along with how long ago the previous train left. From this information, we must work backwards and determine the exact clock time at which the announcement was made.

Given Data / Assumptions:

• Trains for Fatehpur leave Agra station every 2 hours 30 minutes.
• The next train will come at 17:00 hours.
• The previous train left 37 minutes before the announcement time.
• All departures follow the same fixed schedule with no delays.

Concept / Approach:
If trains leave at regular intervals, then the gap between consecutive departures is constant. We know the time of the next departure and the interval, so we can find the time of the previous departure by subtracting the interval from 17:00 hours. Once we know when the previous train left, we subtract the time elapsed since that departure to get the announcement time.

Step-by-Step Solution:
Step 1: Departure interval = 2 hours 30 minutes = 150 minutes. Step 2: Next departure time given = 17:00 hours. Step 3: Previous departure time = 17:00 minus 2 hours 30 minutes = 14:30 hours. Step 4: The announcement states that the train left 37 minutes ago. Step 5: Therefore, announcement time = previous departure time + 37 minutes = 14:30 + 0:37 = 15:07 hours. Step 6: Thus, the announcement must have been made at 15:07 hours.

Verification / Alternative check:
We can verify by checking both sides. From 15:07 to 17:00 is 1 hour 53 minutes. Adding the earlier 37 minutes to reach 2 hours 30 minutes confirms the departure interval of 150 minutes between the previous and the next trains. This consistency ensures that the schedule and announcement information match the calculated time.

Why Other Options Are Wrong:
Times such as 15:00, 15:05, or 15:20 do not keep the exact 2 hour 30 minute gap between the known 17:00 departure and the earlier train when combined with the stated 37 minute offset. The distractor 14:53 does not align correctly with either the interval or the given 37 minute elapsed time.

Common Pitfalls:
A common mistake is to subtract 37 minutes from 17:00 instead of adding it to the previous departure time. Some learners also misconvert the 2 hour 30 minute interval, or accidentally treat 2 hours 30 minutes as 2.3 hours. Keeping everything in minutes and working stepwise avoids confusion.

Final Answer:
The announcement was made at 15:07 hrs.