Question

Trains pass through Park Street station at regular intervals of 45 minutes. A man is standing at the station. He knows that the previous train passed 15 minutes ago, and the next train will arrive at 9:45 AM. What is the current time?

• A. 9:00 AM
• B. 9:15 AM
• C. 9:30 AM
• D. 9:45 AM

Hint:

If events occur every \(T\) minutes and the last event occurred \(x\) minutes ago, then the next event will occur after \(T-x\) minutes.

Answer 1

The Correct Option is A

Concept: Successive trains arrive at a fixed interval of 45 minutes. \[ \text{Train Interval}=45 \text{ minutes} \] The current time can be determined using the information about the previous and next train.

Step 1: Determine the time gap between current time and next train.
The previous train passed 15 minutes ago. Since trains come every 45 minutes, \[ 45-15=30 \text{ minutes} \] So the next train will arrive 30 minutes from now.

Step 2: Use the arrival time of the next train.
Next train arrives at \[ 9:45\ \text{AM} \] Therefore, \[ \text{Current Time}=9:45-30 \text{ minutes} \] \[ =9:15\ \text{AM} \]

Step 3: Verify the condition.
If current time is 9:15 AM, then: \[ 9:15-15\text{ min}=9:00\text{ AM} \] Previous train passed at 9:00 AM. Next train: \[ 9:00+45=9:45\text{ AM} \] Condition satisfied. \[ \boxed{9:15\text{ AM}} \] Hence the correct option is \[ \boxed{(B)} \]