The distance between two stations A and B is 800 km. A train X starts from A and moves towards B at 40 km/h and another train Y starts from B and moves towards A at 60 km/ h. How far from A will they cross each other?

Options

A. 380 km
B. 320 km
C. 300 km
D. 360 km

Answer

To solve the problem of how far from station A the two trains will cross each other, we can follow these steps:

### Step 1: Understand the Problem
We have two trains:
- Train X starts from station A and travels towards station B at a speed of 40 km/h.
- Train Y starts from station B and travels towards station A at a speed of 60 km/h.
The distance between the two stations A and B is 800 km.

### Step 2: Calculate the Combined Speed of the Trains
Since the trains are moving towards each other, we can add their speeds to find the rate at which the distance between them decreases.

\[ \text{Combined Speed} = \text{Speed of Train X} + \text{Speed of Train Y} = 40 \, \text{km/h} + 60 \, \text{km/h} = 100 \, \text{km/h} \]

### Step 3: Calculate the Time Taken to Meet
To find out how long it will take for the two trains to meet, we can use the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Combined Speed}} = \frac{800 \, \text{km}}{100 \, \text{km/h}} = 8 \, \text{hours} \]

### Step 4: Calculate the Distance Covered by Train X
Now, we need to find out how far Train X travels in that time. We can use the formula:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

For Train X:

\[ \text{Distance covered by Train X} = 40 \, \text{km/h} \times 8 \, \text{hours} = 320 \, \text{km} \]

### Step 5: Conclusion
The trains will cross each other 320 km from station A.

### Summary of the Solution
- The distance from station A where the trains cross each other is **320 km**.