Problems on Trains
- 1. 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
Correct Answer: 24 sec
Explanation:
| Relative speed = | = (45 + 30) km/hr | |||||||
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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 |
- 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
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.
- 3. 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
Correct Answer: 82 km/hr
Explanation:
Let the speed of the second train be x km/hr.
| Relative speed | = (x + 50) km/hr | |||||||
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Distance covered = (108 + 112) = 220 m.
| ∴ | 220 | = 6 | ||
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⟹ 250 + 5x = 660
⟹ x = 82 km/hr.
- 4. 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
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 |
- 5. A train runs with a speed of 200 km/hour. What will be its speed in m/sec?
Options- A. 50 m/sec
- B. 55.55 m/sec
- C. 48 m/sec
- D. 66.66 m/sec Discuss
Correct Answer: 55.55 m/sec
Explanation:
Speed in km/ hour =200
Speed in m/sec = 200 x 5/18 = 500/9 m/sec = 55.55 m/sec
- 6. A train crosses a pole in 10 sec and a 200m long platform in 20 sec. What is the length of the train?
Options- A. 100m
- B. 200m
- C. 250m
- D. 300m Discuss
Correct Answer: 200m
Explanation:
Let the length of train be x meter and speed be y m/sec
Therefore, time taken to cross the pole = x/y sec
and time taken to cross the platform = ( Length of train + Length of platform) / speed of train
Therefore x/y = 10
And, (x+200) / y = 20
? 10y + 200 = 20 y
? speed of train, y = 20 m/sec
And length of rain = x = 10y = 200m
- 7. Two trains running at 36 km/hr and 54 km/hr are running parallel in the opposite direction. If their lengths are 200m and 300m respectively. Then how much time will they take to cross each other?
Options- A. 20 sec
- B. 25 sec
- C. 30 sec
- D. 35 sec Discuss
Correct Answer: 20 sec
Explanation:
Relative speed, when the trains are running in the opposite direction = Sum of the speed
Therefore, Relative speed = 36 km/hr +72 km/hr = 90 km/hr
Relative speed in m/sec = 90 km/hr x 5/18= 25 m/sec
Distance covered = sum of the lengths of the train = 200 m+ 300 m = 500m
Therefore, time taken = 500m / 25 m/sec = 20 sec
- 8. A 200 m long train is running at a speed of 60 km/ hr. Find out the time it takes to pass a man standing at the platform
Options- A. 10 sec
- B. 12 sec
- C. 15 sec
- D. 18 sec Discuss
Correct Answer: 12 sec
Explanation:
Speed of the train = (60 x 5/18) m/sec = 50/3 m/sec
Distance covered in passing the standing person = 200m
Required time taken= =200/(50/3) = 200 x (3/50) = 12 sec
- 9. A train is running at the speed of 264 Km/hr. If the length of the train is 330m, then how long will it take to cross a platform which is 330m long?
Options- A. 9 sec
- B. 11 sec
- C. 12 sec
- D. 15 sec Discuss
Correct Answer: 9 sec
Explanation:
Speed of the train = (264 x 5/18) m/sec = 220/3 m/sec
Distance covered in passing the platform = (330+330) m= 660m
Time taken= ( 660 / (220/3) ) sec = (660 x 3/ 220 ) = 9 sec
- 10. A train which is 264 meter long passes a pole in 12 sec. Find out the speed of train?
Options- A. 80 km/hr
- B. 80.6 km/hr
- C. 82.2 km/hr
- D. 79.2 km/hr Discuss
Correct Answer: 79.2 km/hr
Explanation:
Length of train = 264 m
Time taken to cross the pole = 12 sec
Speed of the train, in m/sec = Length of the train/ Time taken to cross the pole
Therefore, speed in m/sec= (264 / 12) m/sec = 22 m /sec
Calculating speed in km/ hour = (22 m/sec ) x 18/5 = 396/5 km/hr = 79.2 km/ hour
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