Problems on Trains
- 1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options- A. 120 metres
- B. 180 metres
- C. 324 metres
- D. 150 metres Discuss
Correct Answer: 150 metres
Explanation:
| Speed = | ❨ | 60 x | 5 | ❩m/sec | = | ❨ | 50 | ❩m/sec. |
| 18 | 3 |
Length of the train = (Speed x Time).
| ∴ Length of the train = | ❨ | 50 | x 9 | ❩m = 150 m. |
| 3 |
- 2. A train travelling at a speed of 75 mph enters a tunnel 3½ miles long. The train is ¼ mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
Options- A. 2.5 min
- B. 3 min
- C. 3.2 min
- D. 3.5 min Discuss
Correct Answer: 3 min
Explanation:
| Total distance covered |
|
|||||||||
|
| ∴ Time taken |
|
|||||||
|
||||||||
|
||||||||
| = 3 min. |
- 3. 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. The length of each train is:
Options- A. 50 m
- B. 72 m
- C. 80 m
- D. 82 m Discuss
Correct Answer: 50 m
Explanation:
Let the length of each train be x metres.
Then, distance covered = 2x metres.
Relative speed = (46 - 36) km/hr
| = | ❨ | 10 x | 5 | ❩m/sec |
| 18 |
| = | ❨ | 25 | ❩m/sec |
| 9 |
| ∴ | 2x | = | 25 |
| 36 | 9 |
⟹ 2x = 100
⟹ x = 50.
- 4. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
Options- A. 9
- B. 9.6
- C. 10
- D. 10.8 Discuss
Correct Answer: 10.8
Explanation:
| Relative speed = (60 + 40) km/hr = | ❨ | 100 x | 5 | ❩m/sec | = | ❨ | 250 | ❩m/sec. |
| 18 | 9 |
Distance covered in crossing each other = (140 + 160) m = 300 m.
| Required time = | ❨ | 300 x | 9 | ❩sec | = | 54 | sec = 10.8 sec. |
| 250 | 5 |
- 5. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
Options- A. 200 m
- B. 225 m
- C. 245 m
- D. 250 m Discuss
Correct Answer: 245 m
Explanation:
| Speed = | ❨ | 45 x | 5 | ❩m/sec | = | ❨ | 25 | ❩m/sec. |
| 18 | 2 |
Time = 30 sec.
Let the length of bridge be x metres.
| Then, | 130 + x | = | 25 |
| 30 | 2 |
⟹ 2(130 + x) = 750
⟹ x = 245 m.
- 6. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options- A. 120 m
- B. 240 m
- C. 300 m
- D. None of these Discuss
Correct Answer: 240 m
Explanation:
| Speed = | ❨ | 54 x | 5 | ❩m/sec = 15 m/sec. |
| 18 |
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
| Then, | x + 300 | = 15 |
| 36 |
⟹ x + 300 = 540
⟹ x = 240 m.
- 7. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
Options- A. 1 : 3
- B. 3 : 2
- C. 3 : 4
- D. None of these Discuss
Correct Answer: 3 : 2
Explanation:
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.
| ∴ | 27x + 17y | = 23 |
| x+ y |
⟹ 27x + 17y = 23x + 23y
⟹ 4x = 6y
| ⟹ | x | = | 3 | . |
| y | 2 |
- 8. A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options- A. 40 sec
- B. 42 sec
- C. 45 sec
- D. 48 sec Discuss
Correct Answer: 40 sec
Explanation:
| Formula for converting from km/hr to m/s: X km/hr = | ❨ | X x | 5 | ❩ | m/s. |
| 18 |
| Therefore, Speed = | ❨ | 45 x | 5 | ❩m/sec | = | 25 | m/sec. |
| 18 | 2 |
Total distance to be covered = (360 + 140) m = 500 m.
| Formula for finding Time = | ❨ | Distance | ❩ |
| Speed |
| ∴ Required time = | ❨ | 500 x 2 | ❩sec | = 40 sec. |
| 25 |
- 9. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
Options- A. 65 sec
- B. 89 sec
- C. 100 sec
- D. 150 sec Discuss
Correct Answer: 89 sec
Explanation:
| Speed = | ❨ | 240 | ❩m/sec = 10 m/sec. |
| 24 |
| ∴ Required time = | ❨ | 240 + 650 | ❩sec = 89 sec. |
| 10 |
- 10. A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
Options- A. 45 m
- B. 50 m
- C. 54 m
- D. 72 m Discuss
Correct Answer: 50 m
Explanation:
| 2 kmph = | ❨ | 2 x | 5 | ❩ | m/sec = | 5 | m/sec. |
| 18 | 9 |
| 4 kmph = | ❨ | 4 x | 5 | ❩ | m/sec = | 10 | m/sec. |
| 18 | 9 |
Let the length of the train be x metres and its speed by y m/sec.
| Then, | ❨ | x | ❩ | = 9 and | ❨ | x | ❩ | = 10. |
|
|
∴ 9y - 5 = x and 10(9y - 10) = 9x
⟹ 9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50.
∴ Length of the train is 50 m.
More in Aptitude:
Programming
Copyright ©CuriousTab. All rights reserved.