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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 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
- 2. 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
- 3. 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
- 4. 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
- 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. Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
Options- A. 12 sec
- B. 24 sec
- C. 48 sec
- D. 60 sec 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. 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 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 Discuss
- 10. A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60°. What is the distance between the base of the tower and the point P?
Options- A. 4√3 units
- B. 8 units
- C. 12 units
- D. Data inadequate
- E. None of these Discuss
Problems on Trains
Search Results
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: 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 |
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: 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: 24 sec
Explanation:
| Relative speed = | = (45 + 30) km/hr | |||||||
|
||||||||
|
We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.
So, distance covered = Length of the slower train.
Therefore, Distance covered = 500 m.
| ∴ Required time = | ❨ | 500 x | 6 | ❩ | = 24 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: 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: 81 km/hr
Explanation:
| 4.5 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 |
Correct Answer: Data inadequate
Explanation:
One of AB, AD and CD must have given.
So, the data is inadequate.
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