Question

A train starts from Delhi at 6:00 AM and reaches Ambala Cantt at 10:00 AM. Another train starts from Ambala Cantt at 8:00 AM and reaches Delhi at 11:30 AM. If the distance between Delhi and Ambala Cantt is 200 km, at what time did the two trains meet each other?

• A. 8:56 AM
• B. 8:46 AM
• C. 7:56 AM
• D. 8:30 AM

Hint:

Account for the 2-hour head start of the first train before setting up the meeting equation.

Answer 1

The Correct Option is A

Here is a second way, thinking in terms of the gap between the trains at 8:00 AM and how fast that gap closes.

1. Speeds. Train 1: $200/4 = 50$ km/h. Train 2: $200/3.5 = 400/7 \approx 57.14$ km/h.
2. Position of Train 1 at 8:00 AM. It has run for 2 hours by then, covering $50\times2=100$ km, so it is 100 km from Ambala Cantt.
3. Gap at 8:00 AM. Train 2 starts exactly at Ambala Cantt at 8:00 AM, so the two trains are 100 km apart at that moment, moving toward each other.
4. Closing speed. $50 + 400/7 = 350/7+400/7 = 750/7$ km/h.
5. Time to close the gap. $\dfrac{100}{750/7} = \dfrac{700}{750} = \dfrac{14}{15}$ hours $\approx 56$ minutes.
6. Meeting time. $8{:}00$ AM $+ 56$ minutes $= 8{:}56$ AM.

This matches the first method exactly, confirming option A. \[ \boxed{8:56\ \text{AM}} \]