Problems On Trains

Question: 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

Answer: Option B

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.

Question:
Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

[A].

36

[B].

45

[C].

48

[D].

49

Answer: Option C

Explanation:

Relative speed = (60+ 90) km/hr

=		150 x	5	m/sec
			18

=		125	m/sec.
		3

Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.

Required time =		2000 x	3	sec = 48 sec.
			125

Question:
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:

[A].

9

[B].

9.6

[C].

10

[D].

10.8

Answer: Option D

Explanation:

Relative speed = (60 + 40) km/hr =		100 x	5	m/sec	=		250	m/sec.
			18				9

Distance covered in crossing each other = (140 + 160) m = 300 m.

Required time =		300 x	9	sec	=	54	sec = 10.8 sec.
			250			5

Question:
A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

[A].

5 sec

[B].

6 sec

[C].

7 sec

[D].

10 sec

Answer: Option B

Explanation:

Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.

=		66 x	5	m/sec
			18

=		55	m/sec.
		3

Time taken to pass the man =		110 x	3	sec = 6 sec.
			55

Question:
A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

[A].

3.6 sec

[B].

18 sec

[C].

36 sec

[D].

72 sec

Answer: Option C

Explanation:

Speed of train relative to jogger = (45 – 9) km/hr = 36 km/hr.

=		36 x	5	m/sec
			18

   = 10 m/sec.

Distance to be covered = (240 + 120) m = 360 m.

Time taken =		360	sec	= 36 sec.
		10

Question: 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

Answer: Option B

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.

Question:
A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

[A].

230 m

[B].

240 m

[C].

260 m

[D].

270 m

Answer: Option D

Explanation:

Speed =		72 x	5	m/sec	= 20 m/sec.
			18

Time = 26 sec.

Let the length of the train be x metres.

Then,	x + 250	= 20
	26

x + 250 = 520

x = 270.

Question: 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

Answer: Option C

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.

Video Explanation: https://youtu.be/M_d8WufJWKc

Question: 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

Answer: Option D

Explanation:

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

Length of the train = (Speed x Time).

Length of the train =		50	x 9	m = 150 m.
		3

Video Explanation: https://youtu.be/q6Xy5JXNp-k

Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

[A].

40 sec

[B].

42 sec

[C].

45 sec

[D].

48 sec

Answer: Option A

Explanation:

Formula for converting from km/hr to m/s:   X km/hr =		X x	5		m/s.
			18

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

Total distance to be covered = (360 + 140) m = 500 m.

Formula for finding Time =		Distance
		Speed

Required time =		500 x 2	sec	= 40 sec.
		25