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Problems on Trains

In solving problems on trains, the following points should be kept in mind. Time taken by a train to cross a pole (or Signal post or, a standing man)

Trains problems

Time taken by a train to cross a bridge (or tunnel or a train at rest or a platform)

Time taken by a train to cross a moving object

where L1 and V1 are the length and speed of the train and L2 and V2 are the length and speed of the moving object.


Solved Examples


1 . A train 300 m long is running with a speed of 54 km/hr. In what time will it cross a telephone pole?
Ans: Speed of the train = 54 x 5/18 m/s
= 15 m/s
Time taken to cross the pole = 300/15 = 20 seconds

2 . A train 220 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
Ans: Time taken to pass the man
Ans:

3. Two trains 80 metres and 120 metres long are running at the rates of 25 km/hr. and 35 km/hr. respectively on parallel rails. If they are moving in same directions, how long will they take to pass each other?
Ans:

PRACTICE TEST

1 . How long will it take for a train 120 m long running at 40 km/hr. to cross a bridge 80 metres long?
1) 18 min   2) 18 seconds   3) 20 seconds  4) 19 seconds

2 . A train running at 50 m/s takes 30 seconds to cross a platform of 800m. long. The length of the train in metres is?
1) 900  2) 300  3) 550  4) 700

3 . A person standing on a platform of length 200 metres observed that a train takes 10 seconds to pass him, passed completely through the platform in 30 seconds. Then the length of the train is?
1) 100 metres  2) 150 metres  3) 80 metres  4) 105 metres

4 . A train running at uniform speed takes 54 seconds to pass a platform of 324 m. long and 45 seconds to pass another platform of 240m. long. The length of the train in metres is?
1) 180  2) 170  3) 190  4) 100

5 . A train 300 m long is running at a speed of 68 km/hr. It will cross a man coming from the opposite direction at a speed of 4km/hr. in?
1) 30 seconds  2) 15 seconds  3) 3: 25 seconds  4) 21.6 seconds

6 . A train 240 metres long, takes 24 seconds to cross a man running at 10 km/hr in the same direction as the train. The speed of the train is?
1) 32 km/hr  2) 46 km/hr  3) 38 km/hr  4) 24 km/hr

7 . A train crosses a platform in 60 seconds travelling at a speed of 54 km/hr. If the length of the platform is 500 metres, what is the length of the train ?
1) 400 m  2) 300 m  3) 450 m  4) 500 m

8 . A man running at 18 km/hr crosses a bridge in 2 minutes. The length of the bridge is ?
1) 1.2 km  2) 0.6 km  3) 1 km  4) 3.6 km

9 . A railway passenger counts the telegraph posts on the line as he passes them. If they are 50 m apart from each other and the train is running at the rate of 48 km/hr. how many posts will he pass per minute?
1) 16  2) 17  3) 18  4) 13

10. Two trains are running at 40 km/hr. and 20 km/hr. respectively in the same direction. The faster train completely passes a man sitting in the slower train in 5 seconds. What is the length of the faster train ?
1) 23 2/9 m  2) 27 m 3) 27 7/9 m  4) 23 m

ANSWERS TO PRACTICE TEST

1 . (2)  2 . (4)  3 . (1)  4 . (1)  5 . (2)  6 . (2)  7 . (1)  8.(2)  9 . (2)  10. (3)

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