## Problem on Trains

#### Problem on Trains

1. A train runs with a speed of 200 km/hour. What will be its speed in m/sec?
1. 50 m/sec
2. 55.55 m/sec
3. 48 m/sec
4. 66.66 m/sec

1. 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

1. A train crosses a pole in 10 sec and a 200m long platform in 20 sec. What is the length of the train?
1. 100m
2. 200m
3. 250m
4. 300m

1. 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 train

##### Correct 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

1. 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?
1. 20 sec
2. 25 sec
3. 30 sec
4. 35 sec

1. 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 = 500m

##### Correct 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

1. 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
1. 10 sec
2. 12 sec
3. 15 sec
4. 18 sec

1. 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

1. 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 ?
1. 9 sec
2. 11 sec
3. 12 sec
4. 15 sec

1. 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