Problems on Trains

Problems on Trains

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Question 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
Question 1 Explanation: 
Speed= (60 x5/18)m/sec =50/3 m/sec. Length of the train = (Speed x Time). Length of the train =(50/3)x 9 m = 150 m.
Question 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
Question 2 Explanation: 
Speed of the train relative to man =(125/10) m/sec =(25/2)m/sec. =((25/2)x(18/5)km/hr = 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.
Question 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
Question 3 Explanation: 
Speed = 45 x(5/18)m/sec =25/2 m/sec. Time = 30 sec. Let the length of bridge be x metres. Then, (130 + x)/30=25/2 => 2(130 + x) = 750 =>x = 245 m.
Question 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
Question 4 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)/(x+ y)= 23 => 27x + 17y = 23x + 23y => 4x = 6y =>> x/y=3/2
Question 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
Question 5 Explanation: 
Speed = 54 x(5/18)m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x metres. Then, (x + 300)/30= 15 ==>x + 300 = 540 ==>x = 240 m.
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