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 goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
Options- A. 230 m
- B. 240 m
- C. 260 m
- D. 270 m Discuss
Correct Answer: 270 m
Explanation:
| Speed = | ❨ | 72 x | 5 | ❩m/sec | = 20 m/sec. |
| 18 |
Time = 26 sec.
Let the length of the train be x metres.
| Then, | x + 250 | = 20 |
| 26 |
⟹ x + 250 = 520
⟹ x = 270.
- 3. 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.
- 4. A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
Options- A. 400 m
- B. 450 m
- C. 560 m
- D. 600 m Discuss
Correct Answer: 400 m
Explanation:
Let the length of the first train be x metres.
| Then, the length of the second train is | ❨ | x | ❩ | metres. |
| 2 |
| Relative speed = (48 + 42) kmph = | ❨ | 90 x | 5 | ❩ | m/sec = 25 m/sec. |
| 18 |
| ∴ | [x + (x/2)] | = 12 or | 3x | = 300 or x = 200. |
| 25 | 2 |
∴ Length of first train = 200 m.
Let the length of platform be y metres.
| Speed of the first train = | ❨ | 48 x | 5 | ❩ | m/sec = | 40 | m/sec. |
| 18 | 3 |
| ∴ (200 + y) x | 3 | = 45 |
| 40 |
⟹ 600 + 3y = 1800
⟹ y = 400 m.
- 5. A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Options- A. 5 sec
- B. 6 sec
- C. 7 sec
- D. 10 sec Discuss
Correct Answer: 6 sec
Explanation:
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.
| = | ❨ | 66 x | 5 | ❩m/sec |
| 18 |
| = | ❨ | 55 | ❩m/sec. |
| 3 |
| ∴ Time taken to pass the man = | ❨ | 110 x | 3 | ❩sec = 6 sec. |
| 55 |
- 6. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
Options- A. 69.5 km/hr
- B. 70 km/hr
- C. 79 km/hr
- D. 79.2 km/hr Discuss
Correct Answer: 79.2 km/hr
Explanation:
Let the length of the train be x metres and its speed by y m/sec.
| Then, | x | = 8 ⟹ x = 8y |
| y |
| Now, | x + 264 | = y |
| 20 |
⟹ 8y + 264 = 20y
⟹ y = 22.
| ∴ Speed = 22 m/sec = | ❨ | 22 x | 18 | ❩ | km/hr = 79.2 km/hr. |
| 5 |
- 7. A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Options- A. 230 m
- B. 240 m
- C. 260 m
- D. 320 m
- E. None of these Discuss
Correct Answer: 230 m
Explanation:
Relative speed = (120 + 80) km/hr
| = | ❨ | 200 x | 5 | ❩m/sec |
| 18 |
| = | ❨ | 500 | ❩m/sec. |
| 9 |
Let the length of the other train be x metres.
| Then, | x + 270 | = | 500 |
| 9 | 9 |
⟹ x + 270 = 500
⟹ x = 230.
- 8. 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.
- 9. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
Options- A. 3.6 sec
- B. 18 sec
- C. 36 sec
- D. 72 sec Discuss
Correct Answer: 36 sec
Explanation:
Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr.
| = | ❨ | 36 x | 5 | ❩m/sec |
| 18 |
= 10 m/sec.
Distance to be covered = (240 + 120) m = 360 m.
- 10. 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 |
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| ∴ Time taken |
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| = 3 min. |
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