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- Question
How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options- A. 25
- B. 30
- C. 40
- D. 45
- Correct Answer
- 30
ExplanationSpeed of the train relative to man = (63 - 3) km/hr = 60 km/hr = ❨ 60 x 5 ❩ m/sec 18 = ❨ 50 ❩ m/sec. 3 ∴ Time taken to pass the man = ❨ 500 x 3 ❩ sec 50 = 30 sec. - 1. Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
Options- A. 10
- B. 18
- C. 36
- D. 72 Discuss
- 2. Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
Options- A. 23 m
- B. 23 2⁄9 m
- C. 27 7⁄9 m
- D. 29 m Discuss
- 3. Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Options- A. 2 : 3
- B. 4 : 3
- C. 6 : 7
- D. 9 : 16 Discuss
- 4. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options- A. 9 a.m.
- B. 10 a.m.
- C. 10.30 a.m.
- D. 11 a.m. Discuss
- 5. 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
- 6. 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
- 7. A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Options- A. 320 m
- B. 350 m
- C. 650 m
- D. Data inadequate Discuss
- 8. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Options- A. 45 km/hr
- B. 50 km/hr
- C. 54 km/hr
- D. 55 km/hr Discuss
- 9. A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
Options- A. 50 m
- B. 150 m
- C. 200 m
- D. Data inadequate Discuss
- 10. 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
Problems on Trains
Search Results
Correct Answer: 36
Explanation:
Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
| So, 2x = | (120 + 120) |
| 12 |
⟹ 2x = 20
⟹ x = 10.
| ∴ Speed of each train = 10 m/sec = | ❨ | 10 x | 18 | ❩ | km/hr = 36 km/hr. |
| 5 |
Correct Answer: 27 7⁄9 m
Explanation:
| Relative speed = (40 - 20) km/hr = | ❨ | 20 x | 5 | ❩ | m/sec = | ❨ | 50 | ❩ | m/sec. |
| 18 | 9 |
| ∴ Length of faster train = | ❨ | 50 | x 5 | ❩ | m = | 250 | m = 27 | 7 | m. |
| 9 | 9 | 9 |
Correct Answer: 4 : 3
Explanation:
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.
Correct Answer: 10 a.m.
Explanation:
Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
∴ 20x + 25(x - 1) = 110
⟹ 45x = 135
⟹ x = 3.
So, they meet at 10 a.m.
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.
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: 350 m
Explanation:
| Speed = | ❨ | 300 | ❩ | m/sec = | 50 | m/sec. |
| 18 | 3 |
Let the length of the platform be x metres.
| Then, | ❨ | x + 300 | ❩ | = | 50 |
| 39 | 3 |
⟹ 3(x + 300) = 1950
⟹ x = 350 m.
Correct Answer: 50 km/hr
Explanation:
| Speed of the train relative to man = | ❨ | 125 | ❩m/sec |
| 10 |
| = | ❨ | 25 | ❩m/sec. |
| 2 |
| = | ❨ | 25 | x | 18 | ❩km/hr |
| 2 | 5 |
= 45 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
∴ x - 5 = 45 ⟹ x = 50 km/hr.
Correct Answer: 150 m
Explanation:
Let the length of the train be x metres and its speed by y m/sec.
| Then, | x | = 15 ⟹ y = | x | . |
| y | 15 |
| ∴ | x + 100 | = | x |
| 25 | 15 |
⟹ 15(x + 100) = 25x
⟹ 15x + 1500 = 25x
⟹ 1500 = 10x
⟹ x = 150 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.
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