A train starts from Delhi at 8 : 00 am & reached Agra at 10 am. Another train starts from Agra at 8 : 00 am & reached Delhi at 11 : 00 am. Find the meeting time ?

Options

A. `12 : 9` am
B. `9 : 12` pm
C. `9 : 12` am
D. `12 : 9` pm

Answer

To find the meeting time of the two trains, we can follow these steps:

### Step 1: Determine the travel times of both trains.
- The train from Delhi starts at 8:00 AM and reaches Agra at 10:00 AM, taking 2 hours.
- The train from Agra starts at 8:00 AM and reaches Delhi at 11:00 AM, taking 3 hours.

**Hint:** Note the departure and arrival times to calculate the travel duration for each train.

### Step 2: Assume a distance between Delhi and Agra.
- Let’s assume the distance between Delhi and Agra is 6 km for simplicity.

**Hint:** You can assume any distance, but it should be the same for both trains.

### Step 3: Calculate the speeds of both trains.
- Speed of the Delhi train = Distance / Time = 6 km / 2 hours = 3 km/h.
- Speed of the Agra train = Distance / Time = 6 km / 3 hours = 2 km/h.

**Hint:** Use the formula Speed = Distance / Time to find the speed of each train.

### Step 4: Calculate the relative speed of the two trains.
- Since the trains are moving towards each other, their relative speed is the sum of their speeds.
- Relative speed = Speed of Delhi train + Speed of Agra train = 3 km/h + 2 km/h = 5 km/h.

**Hint:** When two objects move towards each other, their speeds add up.

### Step 5: Calculate the time taken to meet.
- The time taken to meet = Distance / Relative Speed = 6 km / 5 km/h = 1.2 hours.

**Hint:** Use the formula Time = Distance / Speed to find the time until they meet.

### Step 6: Determine the meeting time.
- Since both trains start at 8:00 AM, we add 1.2 hours (which is 1 hour and 12 minutes) to 8:00 AM.
- 8:00 AM + 1 hour 12 minutes = 9:12 AM.

**Hint:** Convert decimal hours into minutes to add to the starting time correctly.

### Final Answer:
The two trains will meet at **9:12 AM**.