Problem on Trains
 A train runs with a speed of 200 km/hour. What will be its speed in m/sec?

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Speed in m/sec = (Speed in Km/ hour) x 5/18
Correct Option: B
Speed in km/ hour =200
Speed in m/sec = 200 x 5/18 = 500/9 m/sec = 55.55 m/sec
 A train crosses a pole in 10 sec and a 200m long platform in 20 sec. What is the length of the train?

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Time taken to cross the platform = ( Length of train + Length of platform ) / speed of train
And time taken to cross the pole = Length of train/ speed of trainCorrect Option: B
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
 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?

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Relative speed, when the trains are running in the opposite direction = Sum of the speed
Distance covered = sum of the lengths of the train = 200 m+ 300 m = 500mCorrect Option: A
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
 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

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Required time taken = Distance covered in passing the person (in meter) / Speed of train in m/sec
Correct Option: B
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
 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 ?

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Distance covered by train in passing the platform = Length of train + Length of platform
Correct Option: A
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