Aptitude

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

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.