Train X running at 50 km h leaves station A at 11 a.m and train Y running at 90 km/h on parallel tracks leaves station A at 3 p.m. on the same day and in the same direction. After what distance from station A will both the trains be together?

Options

A. 400 km
B. 425 km
C. 430 km
D. 450 km

Answer

To solve the problem, we need to determine the distance from station A where both trains X and Y will meet.

### Step-by-Step Solution:

1. **Identify the speeds and departure times of both trains:**
- Train X speed = 50 km/h, leaves at 11 a.m.
- Train Y speed = 90 km/h, leaves at 3 p.m.

2. **Calculate the time difference between the departures of the two trains:**
- Train Y leaves 4 hours after Train X (from 11 a.m. to 3 p.m.).

3. **Calculate the distance covered by Train X in those 4 hours before Train Y starts:**
- Distance = Speed × Time
- Distance covered by Train X = 50 km/h × 4 hours = 200 km.

4. **Determine the relative speed of Train Y with respect to Train X:**
- Relative speed = Speed of Train Y - Speed of Train X
- Relative speed = 90 km/h - 50 km/h = 40 km/h.

5. **Calculate the time taken by Train Y to catch up with Train X:**
- Time = Distance / Relative Speed
- Time taken by Train Y to catch Train X = 200 km / 40 km/h = 5 hours.

6. **Calculate the distance from station A where both trains will meet:**
- Distance = Speed of Train Y × Time taken to catch Train X
- Distance = 90 km/h × 5 hours = 450 km.

### Final Answer:
Both trains will meet at a distance of **450 km** from station A.

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