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- Question
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
- 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.
- 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. 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
- 7. 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
- 8. 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
- 9. A 270 meter 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
- 10. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
Options- A. 1 : 3
- B. 3 : 2
- C. 3 : 4
- D. None of these Discuss
Problems on Trains
Search Results
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: 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: 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 |
|
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| = 30 sec. |
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.
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: 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: 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: 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: 3 : 2
Explanation:
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.
| ∴ | 27x + 17y | = 23 |
| x+ y |
⟹ 27x + 17y = 23x + 23y
⟹ 4x = 6y
| ⟹ | x | = | 3 | . |
| y | 2 |
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