Problems on Trains are a significant aspect of quantitative aptitude tests, often found in various competitive exams. These questions test the ability to apply the principles of speed, distance, and time to scenarios involving trains. The key to solving these problems lies in understanding the concepts of relative speed and the effect of the train’s length on the time it takes to cross different objects.

# Problems on Trains – Formulas

**Kilometers per Hour to Meters per Second Conversion**

a km/hr = a × 5/18 m/s

**Meters per Second to Kilometers per Hour Conversion**

a m/s = a × 18/5 km/hr

**Time Taken by a Train to Pass a Stationary Point**

Time = Distance / Speed

Here, Distance = Length of the train (l meters)

**Time Taken by a Train to Pass a Stationary Object of Length b Meters**

Time = (l + b) meters / Speed of the Train

**Relative Speed of Two Trains Moving in the Same Direction**

Relative Speed = (u – v) m/s

**Relative Speed of Two Trains Moving in Opposite Directions**

Relative Speed = (u + v) m/s

**Time for Trains to Cross Each Other (Opposite Directions)**

Time = (a + b) / (u + v) sec

Time = (a + b) / (u – v) sec

**Speed Ratio after Crossing Each Other**

Speed Ratio (A’s speed : B’s speed) = b : a

# Problems on Trains Aptitude – Questions and Answers

## 1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

### Answer:

### Explanation:

```
Speed = 60 x 5/18 m/sec = 50/3 m/sec.
Length of the train = (Speed x Time).
Length of the train = 50/3 x 9 m = 150 m.
```

## 2. A 240-meter long train passes a man walking at 3 km/hr in the opposite direction in 8 seconds. What is the speed of the train?

### Answer:

### Explanation:

```
Relative speed = 240/8 m/s = 30 m/s = 30 x 18/5 km/hr = 108 km/hr.
Speed of train = Relative speed + Speed of man.
Speed of train = 108 km/hr + 3 km/hr = 111 km/hr.
```

## 3. Two trains, each 100 meters long, moving in opposite directions, cross each other in 8 seconds. If one train is moving twice as fast as the other, what is the speed of the faster train?

### Answer:

### Explanation:

```
Let the speed of the slower train be x m/s.
Then, speed of the faster train = 2x m/s.
Relative speed = (x + 2x) = 3x m/s.
Distance = 100 + 100 = 200 meters.
Time = 8 seconds.
200 = 3x * 8.
x = 200/24 m/s.
Speed of the faster train = 2x = 100/12 m/s = 25/3 m/s = 25/3 x 18/5 km/hr = 30 km/hr.
```

## 4. A train 125 meters long takes 5 seconds to pass a man running at 5 km/hr in the same direction. What is the speed of the train?

### Answer:

### Explanation:

```
Relative speed = 125/5 m/s = 25 m/s = 25 x 18/5 km/hr = 90 km/hr.
Speed of train = Relative speed + Speed of man.
Speed of train = 90 km/hr + 5 km/hr = 95 km/hr.
```

## 5. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. What is the length of each train?

### Answer:

### Explanation:

```
Relative speed = (46 - 36) km/hr = 10 km/hr = 10 x 5/18 m/s = 25/9 m/s.
Let the length of each train be L meters.
Total distance covered = L + L = 2L meters.
Time = 36 seconds.
2L = 25/9 x 36.
L = (25/9 x 36) / 2 = 100 meters.
```

## 6. A train traveling at 45 km/hr takes 20 seconds to pass a platform 100 meters long. What is the length of the train?

### Answer:

### Explanation:

```
Speed = 45 x 5/18 m/sec = 25/2 m/sec.
Time = 20 seconds.
Distance covered = Speed x Time = 25/2 x 20 m = 250 meters.
Length of the train = Total distance - Length of platform = 250 m - 100 m = 150 m.
```

## 7. Two trains running in the same direction at 50 km/hr and 30 km/hr completely pass one another in 1 minute. If the length of the first train is 150 meters, what is the length of the second train?

### Answer:

### Explanation:

```
Relative speed = (50 - 30) km/hr = 20 km/hr = 20 x 5/18 m/s = 50/9 m/s.
Time = 1 minute = 60 seconds.
Total distance covered = Relative speed x Time = 50/9 x 60 m = 333.33 meters.
Length of second train = Total distance - Length of first train = 333.33 m - 150 m = 183.33 m ≈ 180 meters.
```

## 8. A train crosses a 350-meter bridge in 35 seconds. If the speed of the train is 54 km/hr, what is the length of the train?

### Answer:

### Explanation:

```
Speed = 54 x 5/18 m/sec = 15 m/sec.
Time = 35 seconds.
Distance covered = Speed x Time = 15 x 35 m = 525 meters.
Length of the train = Total distance - Length of bridge = 525 m - 350 m = 175 m.
```

## 9. A 300-meter long train crosses another train of length 200 meters, traveling in the opposite direction in 10 seconds. If the speed of the second train is 72 km/hr, what is the speed of the first train?

### Answer:

### Explanation:

```
Speed of second train = 72 km/hr = 72 x 5/18 m/s = 20 m/s.
Total distance = Length of first train + Length of second train = 300 m + 200 m = 500 m.
Time = 10 seconds.
Relative speed = Total distance / Time = 500/10 m/s = 50 m/s.
Speed of first train = Relative speed - Speed of second train = 50 m/s - 20 m/s = 30 m/s = 30 x 18/5 km/hr = 108 km/hr.
```

## 10. A train takes 18 seconds to pass completely through a station 162 meters long. If the train is traveling at a speed of 54 km/hr, what is the length of the train?

### Answer:

### Explanation:

```
Speed = 54 x 5/18 m/sec = 15 m/sec.
Time = 18 seconds.
Distance covered = Speed x Time = 15 x 18 m = 270 meters.
Length of the train = Total distance - Length of station = 270 m - 162 m = 108 m.
```

## 11. A train 280 meters long is running at a speed of 60 km/hr. In what time will it pass a bridge 220 meters long?

### Answer:

### Explanation:

```
Speed = 60 x 5/18 m/sec = 50/3 m/sec.
Total distance = Length of train + Length of bridge = 280 m + 220 m = 500 m.
Time = Distance / Speed = 500 m / (50/3) m/sec = 30 seconds.
```

## 12. A 200-meter long train crosses a signal pole in 10 seconds. What is the speed of the train?

### Answer:

### Explanation:

```
Speed = Distance / Time = 200 m / 10 s = 20 m/s.
Speed in km/hr = 20 m/s x 18/5 = 72 km/hr.
```

## 13. Two trains, 150 meters and 100 meters long, run at the speeds of 60 km/hr and 40 km/hr respectively in the same direction. How long will they take to cross each other?

### Answer:

### Explanation:

```
Relative speed = (60 - 40) km/hr = 20 km/hr = 20 x 5/18 m/s = 50/9 m/s.
Total distance = 150 m + 100 m = 250 m.
Time = Distance / Relative speed = 250 m / (50/9) m/s = 45 seconds.
```

## 14. A train 300 meters long is running at a speed of 90 km/hr. How long will it take to cross a 200 meter long bridge?

### Answer:

### Explanation:

```
Speed = 90 x 5/18 m/sec = 25 m/sec.
Total distance = Length of train + Length of bridge = 300 m + 200 m = 500 m.
Time = Distance / Speed = 500 m / 25 m/sec = 20 seconds.
```

## 15. A train running at the speed of 72 km/hr crosses a platform in 27 seconds. The length of the platform is 240 meters. What is the length of the train?

### Answer:

### Explanation:

```
Speed = 72 x 5/18 m/sec = 20 m/sec.
Time = 27 seconds.
Distance covered = Speed x Time = 20 m/sec x 27 s = 540 meters.
Length of the train = Total distance - Length of platform = 540 m - 240 m = 300 m.
```

## 16. Two trains of equal length are running on parallel tracks in opposite directions at 44 km/hr and 32 km/hr. The faster train passes the slower train in 10 seconds. What is the length of each train?

### Answer:

### Explanation:

```
Relative speed = (44 + 32) km/hr = 76 km/hr = 76 x 5/18 m/s = 380/18 m/s.
Total distance covered = Length of one train + Length of other train = 2 x Length of one train.
Time = 10 seconds.
2 x Length of one train = (380/18) m/s x 10 s = 211.11 meters.
Length of one train = 211.11 m / 2 = 105.56 m ≈ 106 meters.
```

## 17. A train running at the speed of 50 km/hr crosses a pole in 18 seconds. What is the length of the train?

### Answer:

### Explanation:

```
Speed = 50 x 5/18 m/sec = 250/18 m/sec.
Length of the train = (Speed x Time).
Length of the train = (250/18) x 18 m = 250 m.
```

## 18. A train takes 12 seconds to pass a stationary person and 20 seconds to pass a platform 100 meters long. What is the length of the train?

### Answer:

### Explanation:

```
Let the length of the train be L meters.
Time to pass a stationary person = 12 seconds.
Speed of the train = L/12 m/s.
Time to pass the platform = 20 seconds.
Distance covered = L + 100 meters.
L + 100 = (L/12) x 20.
Solving for L, L = 100 meters.
```

## 19. Two trains, one 160 meters and the other 140 meters long, are running in opposite directions on parallel tracks. If their speeds are 60 km/hr and 50 km/hr respectively, in how much time will they cross each other?

### Answer:

### Explanation:

```
Relative speed = (60 + 50) km/hr = 110 km/hr = 110 x 5/18 m/s = 305/18 m/s.
Total distance = 160 m + 140 m = 300 m.
Time = Distance / Relative speed = 300 m / (305/18) m/s = 10 seconds.
```

## 20. A 150-meter long train moving at a speed of 75 km/hr crosses a bridge in 30 seconds. What is the length of the bridge?

### Answer:

### Explanation:

```
Speed = 75 x 5/18 m/sec = 125/6 m/sec.
Time = 30 seconds.
Distance covered = Speed x Time = (125/6) m/sec x 30 s = 625 meters.
Length of the bridge = Total distance - Length of train = 625 m - 150 m = 475 m.
```

## 21. A train 200 meters long is running at a speed of 40 km/hr. How long will it take to cross another train 300 meters long running in the opposite direction at a speed of 60 km/hr?

### Answer:

### Explanation:

```
Relative speed = (40 + 60) km/hr = 100 km/hr = 100 x 5/18 m/s = 250/9 m/s.
Total distance = 200 m + 300 m = 500 m.
Time = Distance / Relative speed = 500 m / (250/9) m/s = 18 seconds.
```

## 22. A train moving at a speed of 72 km/hr crosses a platform in 30 seconds. The length of the platform is equal to the length of the train. What is the length of the train?

### Answer:

### Explanation:

```
Speed = 72 x 5/18 m/sec = 20 m/sec.
Let the length of the train be L meters.
Total distance = L + L = 2L meters.
Time = 30 seconds.
2L = 20 m/sec x 30 s = 600 meters.
Length of the train = L = 600 m / 2 = 300 meters.
```

## 23. A 250-meter long train crosses another 200-meter long train running in the same direction in 36 seconds. If the speed of the first train is 30 km/hr, what is the speed of the second train?

### Answer:

### Explanation:

```
Speed of first train = 30 km/hr = 30 x 5/18 m/s = 25/3 m/s.
Total distance = 250 m + 200 m = 450 m.
Time = 36 seconds.
Relative speed = Distance / Time = 450 m / 36 s = 12.5 m/s.
Speed of second train = Speed of first train - Relative speed = (25/3) m/s - 12.5 m/s = (25/3 - 37.5/3) m/s = 12.5/3 m/s = 12.5/3 x 18/5 km/hr = 15 km/hr.
```

## 24. Two trains 150 meters and 200 meters long are running towards each other on parallel tracks at 40 km/hr and 32 km/hr respectively. In how much time will they cross each other?

### Answer:

### Explanation:

```
Relative speed = (40 + 32) km/hr = 72 km/hr = 72 x 5/18 m/s = 20 m/s.
Total distance = 150 m + 200 m = 350 m.
Time = Distance / Relative speed = 350 m / 20 m/s = 17.5 seconds.
```

## 25. A train running at the speed of 54 km/hr takes 20 seconds to pass a platform. The length of the platform is twice the length of the train. What is the length of the train?

### Answer:

### Explanation:

```
Speed = 54 x 5/18 m/sec = 15 m/sec.
Let the length of the train be L meters.
Length of the platform = 2L meters.
Total distance = L + 2L = 3L meters.
Time = 20 seconds.
3L = 15 m/sec x 20 s = 300 meters.
Length of the train = L = 300 m / 3 = 100 meters.
```