Problems on Trains

Question: Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
[A].

2 : 3

[B].

4 : 3

[C].

6 : 7

[D].

9 : 16

Answer: Option B

Explanation:

Let us name the trains as A and B. Then,

(A’s speed) : (B’s speed) = b : a = 16 : 9 = 4 : 3.

Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
[A].

9 a.m.

[B].

10 a.m.

[C].

10.30 a.m.

[D].

11 a.m.

Answer: Option B

Explanation:

Suppose they meet x hours after 7 a.m.

Distance covered by A in x hours = 20x km.

Distance covered by B in (x – 1) hours = 25(x – 1) km.

20x + 25(x – 1) = 110

45x = 135

x = 3.

So, they meet at 10 a.m.

Question: A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
[A].

400 m

[B].

450 m

[C].

560 m

[D].

600 m

Answer: Option A

Explanation:

Let the length of the first train be x metres.

Then, the length of the second train is		x		metres.
		2

Relative speed = (48 + 42) kmph =		90 x	5		m/sec = 25 m/sec.
			18

	[x + (x/2)]	= 12 or	3x	= 300     or     x = 200.
	25		2

Length of first train = 200 m.

Let the length of platform be y metres.

Speed of the first train =		48 x	5		m/sec =	40	m/sec.
			18			3

(200 + y) x	3	= 45
	40

600 + 3y = 1800

y = 400 m.

Question: A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
[A].

66 km/hr

[B].

72 km/hr

[C].

78 km/hr

[D].

81 km/hr

Answer: Option D

Explanation:

4.5 km/hr =		4.5 x	5		m/sec =	5	m/sec = 1.25 m/sec, and
			18			4

5.4 km/hr =		5.4 x	5		m/sec =	3	m/sec = 1.5 m/sec.
			18			2

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

Then, (x – 1.25) x 8.4 = (x – 1.5) x 8.5

8.4x – 10.5 = 8.5x – 12.75

0.1x = 2.25

x = 22.5

Speed of the train =		22.5 x	18		km/hr = 81 km/hr.
			5

Question: A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
[A].

45 m

[B].

50 m

[C].

54 m

[D].

72 m

Answer: Option B

Explanation:

2 kmph =		2 x	5		m/sec =	5	m/sec.
			18			9

4 kmph =		4 x	5		m/sec =	10	m/sec.
			18			9

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

Then,		x		= 9 and		x		= 10.
		y – 5 9				y – 10 9

9y – 5 = x and 10(9y – 10) = 9x

9y – x = 5 and 90y – 9x = 100.

On solving, we get: x = 50.

Length of the train is 50 m.

Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
[A].

23 m

[B].

23	2	m
	9

[C].

27	7	m
	9

[D].

29 m

Answer: Option C

Explanation:

Relative speed = (40 – 20) km/hr =		20 x	5		m/sec =		50		m/sec.
			18				9

Length of faster train =		50	x 5		m =	250	m = 27	7	m.
		9				9		9

Question: A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:
[A].

48 km/hr

[B].

54 km/hr

[C].

66 km/hr

[D].

82 km/hr

Answer: Option D

Explanation:

Let the speed of the second train be x km/hr.

Relative speed	= (x + 50) km/hr
	= (x + 50) x 5 m/sec 18
	= 250 + 5x m/sec. 18

Distance covered = (108 + 112) = 220 m.

	220	= 6
	250 + 5x 18

250 + 5x = 660

x = 82 km/hr.

Question: Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
[A].

10

[B].

12

[C].

15

[D].

20

Answer: Option B

Explanation:

Speed of the first train =		120		m/sec = 12 m/sec.
		10

Speed of the second train =		120		m/sec = 8 m/sec.
		15

Relative speed = (12 + 8) = 20 m/sec.

Required time =		(120 + 120)		sec = 12 sec.
		20

Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
[A].

10

[B].

18

[C].

36

[D].

72

Answer: Option C

Explanation:

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

Then, relative speed of the two trains = 2x m/sec.

So, 2x =	(120 + 120)
	12

2x = 20

x = 10.

Speed of each train = 10 m/sec =		10 x	18		km/hr = 36 km/hr.
			5

Question: Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
[A].

12 sec

[B].

24 sec

[C].

48 sec

[D].

60 sec

Answer: Option B

Explanation:

Relative speed =	= (45 + 30) km/hr
	= 75 x 5 m/sec 18
	= 125 m/sec. 6

We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.

So, distance covered = Length of the slower train.

Therefore, Distance covered = 500 m.

Required time =		500 x	6		= 24 sec.
			125