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- Question
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
- Correct Answer
- 50 m
Explanation2 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. y - 5 9 y - 10 9 ∴ 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.
- 1. 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
- 2. 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
- 3. 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
- 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
- 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
- 6. 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
- 7. 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
- 8. A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:
Options- A. 48 km/hr
- B. 54 km/hr
- C. 66 km/hr
- D. 82 km/hr Discuss
- 9. A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:
Options- A. 130
- B. 360
- C. 500
- D. 540 Discuss
- 10. 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
Problems on Trains
Search Results
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.
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 |
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 |
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.
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.
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.
Correct Answer: 3 min
Explanation:
| Total distance covered |
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| ∴ Time taken |
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| = 3 min. |
Correct Answer: 82 km/hr
Explanation:
Let the speed of the second train be x km/hr.
| Relative speed | = (x + 50) km/hr | |||||||
|
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|
Distance covered = (108 + 112) = 220 m.
| ∴ | 220 | = 6 | ||
|
⟹ 250 + 5x = 660
⟹ x = 82 km/hr.
Correct Answer: 500
Explanation:
| Speed = | ❨ | 78 x | 5 | ❩ | m/sec | = | ❨ | 65 | ❩ | m/sec. |
| 18 | 3 |
Time = 1 minute = 60 seconds.
Let the length of the tunnel be x metres.
| Then, | ❨ | 800 + x | ❩ | = | 65 |
| 60 | 3 |
⟹ 3(800 + x) = 3900
⟹ x = 500.
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.
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