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

Options

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

Answer

To solve the problem of when the two trains meet, we can follow these steps:

### Step 1: Calculate the speed of Train A
Train A travels from Delhi to Ambala Cantt, covering a distance of 200 km in 4 hours (from 6 AM to 10 AM).

Speed of Train A = Distance / Time = 200 km / 4 hours = 50 km/h.

### Step 2: Calculate the speed of Train B
Train B travels from Ambala Cantt to Delhi, covering the same distance of 200 km in 3.5 hours (from 8 AM to 11:30 PM).

Speed of Train B = Distance / Time = 200 km / 3.5 hours = 57.14 km/h (approximately).

### Step 3: Determine the time difference between the two trains
Train A starts at 6 AM, and Train B starts at 8 AM. Therefore, Train A has a 2-hour head start.

### Step 4: Calculate the distance covered by Train A in 2 hours
Distance covered by Train A in 2 hours = Speed × Time = 50 km/h × 2 hours = 100 km.

### Step 5: Calculate the remaining distance between the two trains when Train B starts
When Train B starts at 8 AM, Train A has already covered 100 km, so the remaining distance between them is:
200 km - 100 km = 100 km.

### Step 6: Calculate the relative speed of the two trains
Since both trains are moving towards each other, we can add their speeds to find the relative speed.

Relative Speed = Speed of Train A + Speed of Train B = 50 km/h + 57.14 km/h = 107.14 km/h (approximately).

### Step 7: Calculate the time taken to meet
Time taken to meet = Remaining Distance / Relative Speed = 100 km / 107.14 km/h = 0.933 hours (approximately).

To convert this to minutes, we multiply by 60:
0.933 hours × 60 minutes/hour ≈ 56 minutes.

### Step 8: Determine the meeting time
Since Train B starts at 8 AM and it takes approximately 56 minutes for the trains to meet, the meeting time will be:
8:00 AM + 56 minutes = 8:56 AM.

### Final Answer
The two trains meet each other at approximately **8:56 AM**.

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