Problems on Trains
Problems on Trains - Important Points
| 11. | 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: |
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A. 10
B. 18
C. 36
D. 72
View Answer Discuss Work SpaceAnswer: option c
Explanation:
Given, Length of each train = 120 metres.
Let the speed of each train be x m/sec.
Then, relative speed of the two trains = x + x = 2x m/sec.
So, Speed = Distance / Time
=> Relative Speed of two trains = (Sum of length of two trains) / Time taken to cross each other
=> 2x = (120 + 120 ) / 12
=> 2x = 20
=> x = 10 m/sec = 10 x (18 / 5) = 36 km/hr
| 12. | 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. |
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A. 12 sec
B. 24 sec
C. 48 sec
D. 60 sec
View Answer Discuss Work SpaceAnswer: option b
Explanation:
Relative speed = (45 + 30) km/hr = ( 75 x 5/18 ) m/sec = (125/6 ) m/sec
Note: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. Therefore Required time = ( 500 x 6/125 ) = 24 sec.
| 13. | 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? |
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A. 25
B. 30
C. 40
D. 45
View Answer Discuss Work SpaceAnswer: option b
Explanation:
Given, Length of the train = 500 m
Speed of the man = 3 km/hr
Speed of the train = 63 km/hr
Time taken by the train to cross a man = Length of the train / (speed of the train – speed of the man)
=> Time = 500 m / (63 – 3) km/hr
=> Time = 500 m / 60 km/hr
(to convert 60 km/hr to m/sec)
=> Time = 500 m / [60 * (5/18) m/sec]
=> Time = {500 / [60 * (5/18)]} sec
=> Time = {(500 * 18) / (60 * 5)} sec
=> Time = 30 sec
| 14. | 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? |
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A. 69.5 km/hr
B. 70 km/hr
C. 79 km/hr
D. 79.2 km/hr
View Answer Discuss Work SpaceAnswer: option d
Explanation:
Let the length of the train be x metres and its speed by y m/sec.
Time = Length / Speed of the train
Given,A train moves past a telegraph post in 8 seconds.
Then, x/y = 8
=> x = 8y
Now, the same train moves past a bridge of 264 m long in 20 seconds.
=> (x + 264) / y = 20
Substituting x = 8y in the above eqn, we get
=> (8y + 264) = 20y
=> 20y - 8y = 264
=> 12y = 264
=> y = 22.
Therefore Speed = 22 m/sec = ( 22 x 18 /5) km/hr = 79.2 km/hr.
| 15. | A running train overtakes a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is: |
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A. 50 m
B. 150 m
C. 200 m
D. Data inadequate
View Answer Discuss Work SpaceAnswer: option b
Explanation:
Given time taken by train to pass the pole = 15 seconds
=> 15 = Length of train/ speed of train
=> speed of train = Length of train /15 ---> eqn(1)
Given, time taken by train to pass the platform of 100 m long = 25 seconds
=> Time = (Length of train + Length of the platform) / speed of train
=> 25 = (Length of train + 100) /speed of train
Substituting eqn (1) in the above eqn, we get
=> 25 = (Length of train + 100) / (Length of train /15)
=> 25 * (Length of train /15) = (Length of train + 100)
=> (5 / 3) *Length of train = (Length of train + 100)
=> 5*Length of train = 3 (Length of train + 100)
=> 5*Length of train = 3*Length of train + 300
=> 2*Length of train = 300
=> Length of train = 150 meter.
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