# Problems on Trains

1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
 A. 120 metres B. 180 metres C. 324 metres D. 150 metres

Explanation:

 Speed= 60 x 5 m/sec = 50 m/sec. 18 3

 Length of the train = (Speed x Time) = 50 x 9 m = 150 m. 3

2. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
 A. 45 km/hr B. 50 km/hr C. 54 km/hr D. 55 km/hr

Explanation:

 Speed of the train relative to man = 125 m/sec 10

 = 25 m/sec. 2

 = 25 x 18 km/hr 2 5

= 45 km/hr.

Let the speed of the train be x km/hr. Then, relative speed = (x – 5) km/hr. x – 5 = 45 x = 50 km/hr.

3. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
 A. 200 m B. 225 m C. 245 m D. 250 m

Explanation:

 Speed = 45 x 5 m/sec = 25 m/sec. 18 2

Time = 30 sec.

Let the length of bridge be x metres.

 Then, 130 + x = 25 30 2 2(130 + x) = 750 x = 245 m.

4. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
 A. 1 : 3 B. 3 : 2 C. 3 : 4 D. None of these

Explanation:

Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, length of the first train = 27x metres,

and length of the second train = 17y metres. 27x + 17y = 23 x+ y 27x + 17y = 23x + 23y 4x = 6y x = 3 . y 2

5. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
 A. 120 m B. 240 m C. 300 m D. None of these

Explanation:

 Speed = 54 x 5 m/sec = 15 m/sec. 18

Length of the train = (15 x 20)m = 300 m.

Let the length of the platform be x metres.

 Then, x + 300 = 15 36 x + 300 = 540 x = 240 m.