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- Question
A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
Options- A. 66 km/hr
- B. 72 km/hr
- C. 78 km/hr
- D. 81 km/hr
- Correct Answer
- 81 km/hr
Explanation4.5 km/hr = ❨ 4.5 x 5 ❩ m/sec = 5 m/sec = 1.25 m/sec, and 18 4 5.4 km/hr = ❨ 5.4 x 5 ❩ m/sec = 3 m/sec = 1.5 m/sec. 18 2 Let the speed of the train be x m/sec.
Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5
⟹ 8.4x - 10.5 = 8.5x - 12.75
⟹ 0.1x = 2.25
⟹ x = 22.5
∴ Speed of the train = ❨ 22.5 x 18 ❩ km/hr = 81 km/hr. 5 - 1. Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Options- A. 10
- B. 12
- C. 15
- D. 20 Discuss
- 2. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:
Options- A. 36
- B. 45
- C. 48
- D. 49 Discuss
- 3. 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
- 4. 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
- 5. 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
- 6. 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
- 7. 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
- 8. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:
Options- A. 36
- B. 45
- C. 48
- D. 49 Discuss
- 9. Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:
Options- A. 30 km/hr
- B. 45 km/hr
- C. 60 km/hr
- D. 75 km/hr Discuss
- 10. 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
Problems on Trains
Search Results
Correct Answer: 12
Explanation:
| Speed of the first train = | ❨ | 120 | ❩ | m/sec = 12 m/sec. |
| 10 |
| Speed of the second train = | ❨ | 120 | ❩ | m/sec = 8 m/sec. |
| 15 |
Relative speed = (12 + 8) = 20 m/sec.
| ∴ Required time = | [ | (120 + 120) | ] | sec = 12 sec. |
| 20 |
Correct Answer: 48
Explanation:
Relative speed = (60+ 90) km/hr
| = | ❨ | 150 x | 5 | ❩m/sec |
| 18 |
| = | ❨ | 125 | ❩m/sec. |
| 3 |
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
| Required time = | ❨ | 2000 x | 3 | ❩sec = 48 sec. |
| 125 |
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: 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: 3 min
Explanation:
| Total distance covered |
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| ∴ Time taken |
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| = 3 min. |
Correct Answer: 89 sec
Explanation:
| Speed = | ❨ | 240 | ❩m/sec = 10 m/sec. |
| 24 |
| ∴ Required time = | ❨ | 240 + 650 | ❩sec = 89 sec. |
| 10 |
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: 48
Explanation:
Relative speed = (60+ 90) km/hr
| = | ❨ | 150 x | 5 | ❩m/sec |
| 18 |
| = | ❨ | 125 | ❩m/sec. |
| 3 |
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
| Required time = | ❨ | 2000 x | 3 | ❩sec = 48 sec. |
| 125 |
Correct Answer: 60 km/hr
Explanation:
Let the speed of the slower train be x m/sec.
Then, speed of the faster train = 2x m/sec.
Relative speed = (x + 2x) m/sec = 3x m/sec.
| ∴ | (100 + 100) | = 3x |
| 8 |
⟹ 24x = 200
| ⟹ x = | 25 | . |
| 3 |
| So, speed of the faster train = | 50 | m/sec |
| 3 |
| = | ❨ | 50 | x | 18 | ❩km/hr |
| 3 | 5 |
= 60 km/hr.
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 |
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