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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 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
- 2. 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
- 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
- 4. 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
- 5. 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
- 6. 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 Discuss
- 7. 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
- 8. 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
- 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. 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
Problems on Trains
Search Results
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: 82 km/hr
Explanation:
Let the speed of the second train be x km/hr.
| Relative speed | = (x + 50) km/hr | |||||||
|
||||||||
|
Distance covered = (108 + 112) = 220 m.
| ∴ | 220 | = 6 | ||
|
⟹ 250 + 5x = 660
⟹ x = 82 km/hr.
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.
Correct Answer: 89 sec
Explanation:
| Speed = | ❨ | 240 | ❩m/sec = 10 m/sec. |
| 24 |
| ∴ Required time = | ❨ | 240 + 650 | ❩sec = 89 sec. |
| 10 |
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 |
Correct Answer: 30
Explanation:
| Speed of the train relative to man | = (63 - 3) km/hr | |||||||
| = 60 km/hr | ||||||||
|
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|
||||||||
| ∴ Time taken to pass the man |
|
|||||||
| = 30 sec. |
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: 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: 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: 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.
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