Problems on Trains

Question: How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
[A].

25

[B].

30

[C].

40

[D].

45

Answer: Option B

Explanation:

Speed of the train relative to man	= (63 – 3) km/hr
	= 60 km/hr
	= 60 x 5 m/sec 18
	= 50 m/sec. 3
Time taken to pass the man	= 500 x 3 sec 50
	= 30 sec.

Question: A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
[A].

69.5 km/hr

[B].

70 km/hr

[C].

79 km/hr

[D].

79.2 km/hr

Answer: Option D

Explanation:

Let the length of the train be x metres and its speed by y m/sec.

Then,	x	= 8         x = 8y
	y

Now,	x + 264	= y
	20

8y + 264 = 20y

y = 22.

Speed = 22 m/sec =		22 x	18		km/hr = 79.2 km/hr.
			5

Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
[A].

50 m

[B].

150 m

[C].

200 m

[D].

Data inadequate

Answer: Option B

Explanation:

Let the length of the train be x metres and its speed by y m/sec.

Then,	x	= 15         y =	x	.
	y		15

	x + 100	=	x
	25		15

15(x + 100) = 25x

15x + 1500 = 25x

1500 = 10x

x = 150 m.

Question: A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
[A].

320 m

[B].

350 m

[C].

650 m

[D].

Data inadequate

Answer: Option B

Explanation:

Speed =		300		m/sec =	50	m/sec.
		18			3

Let the length of the platform be x metres.

Then,		x + 300		=	50
		39			3

3(x + 300) = 1950

x = 350 m.

Question: A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:
[A].

130

[B].

360

[C].

500

[D].

540

Answer: Option C

Explanation:

Speed =		78 x	5		m/sec	=		65		m/sec.
			18					3

Time = 1 minute = 60 seconds.

Let the length of the tunnel be x metres.

Then,		800 + x		=	65
		60			3

3(800 + x) = 3900

x = 500.

Question: A train travelling at a speed of 75 mph enters a tunnel 3 miles long. The train is mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
[A].

2.5 min

[B].

3 min

[C].

3.2 min

[D].

3.5 min

Answer: Option B

Explanation:

Total distance covered	= 7 + 1 miles 2 4
	= 15 miles. 4

Time taken	= 15 hrs 4 x 75
	= 1 hrs 20
	= 1 x 60 min. 20
	= 3 min.

Question:
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

Answer: Option B

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

Question:
Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:

[A].

30 km/hr

[B].

45 km/hr

[C].

60 km/hr

[D].

75 km/hr

Answer: Option C

Explanation:

Let the speed of the slower train be x m/sec.

Then, speed of the faster train = 2x m/sec.

Relative speed = (x + 2x) m/sec = 3x m/sec.

	(100 + 100)	= 3x
	8

24x = 200

x =	25	.
	3

So, speed of the faster train =	50	m/sec
	3

=		50	x	18	km/hr
		3		5

   = 60 km/hr.

Question:
A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

[A].

230 m

[B].

240 m

[C].

260 m

[D].

320 m

Answer: Option A

Explanation:

Relative speed = (120 + 80) km/hr

=		200 x	5	m/sec
			18

=		500	m/sec.
		9

Let the length of the other train be x metres.

Then,	x + 270	=	500
	9		9

x + 270 = 500

x = 230.

Question:
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:

[A].

50 m

[B].

72 m

[C].

80 m

[D].

82 m

Answer: Option A

Explanation:

Let the length of each train be x metres.

Then, distance covered = 2x metres.

Relative speed = (46 – 36) km/hr

=		10 x	5	m/sec
			18

=		25	m/sec
		9

	2x	=	25
	36		9

2x = 100

x = 50.