A train started from Jaipur at 5 : 00 AM and reach Chandigarh at 9 : 00 AM another train started from Chandigarh at 7 : 00 AM and reached Jaipur at 10 : 30 AM then find the time at which both the trains meet each other ?

Options

A. `7 : 26` AM
B. `8 : 56` AM
C. `8 : 26` AM
D. `7 : 56` AM

Answer

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

### Step 1: Determine the travel times and speeds of both trains.
1. **Train A** (from Jaipur to Chandigarh):
- Departure: 5:00 AM
- Arrival: 9:00 AM
- Total travel time = 4 hours

2. **Train B** (from Chandigarh to Jaipur):
- Departure: 7:00 AM
- Arrival: 10:30 AM
- Total travel time = 3.5 hours (or 7/2 hours)

### Step 2: Assume a distance between Jaipur and Chandigarh.
Let's assume the distance between Jaipur and Chandigarh is 280 km (a multiple of both travel times).

### Step 3: Calculate the speeds of both trains.
1. **Speed of Train A (S1)**:
\[ S1 = \frac{\text{Distance}}{\text{Time}} = \frac{280 \text{ km}}{4 \text{ hours}} = 70 \text{ km/h} \]

2. **Speed of Train B (S2)**:
\[ S2 = \frac{\text{Distance}}{\text{Time}} = \frac{280 \text{ km}}{3.5 \text{ hours}} = 80 \text{ km/h} \]

### Step 4: Calculate the distance covered by Train A by 7:00 AM.
- Train A travels for 2 hours (from 5:00 AM to 7:00 AM):
\[ \text{Distance covered by Train A} = S1 \times \text{Time} = 70 \text{ km/h} \times 2 \text{ hours} = 140 \text{ km} \]

### Step 5: Determine the remaining distance when Train B starts.
- The remaining distance between the two trains when Train B starts at 7:00 AM is:
\[ \text{Remaining distance} = 280 \text{ km} - 140 \text{ km} = 140 \text{ km} \]

### Step 6: Calculate the relative speed of the two trains.
- Since both trains are moving towards each other, their relative speed is:
\[ \text{Relative Speed} = S1 + S2 = 70 \text{ km/h} + 80 \text{ km/h} = 150 \text{ km/h} \]

### Step 7: Calculate the time taken to meet.
- The time taken to cover the remaining distance of 140 km at a relative speed of 150 km/h is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{140 \text{ km}}{150 \text{ km/h}} = \frac{14}{15} \text{ hours} \]

### Step 8: Convert the time into minutes.
- To convert \(\frac{14}{15}\) hours into minutes:
\[ \frac{14}{15} \text{ hours} \times 60 \text{ minutes/hour} = 56 \text{ minutes} \]

### Step 9: Determine the meeting time.
- Since Train B starts at 7:00 AM, adding 56 minutes gives:
\[ 7:00 AM + 56 \text{ minutes} = 7:56 AM \]

### Final Answer:
Both trains meet at **7:56 AM**.