Aptitude

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.

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