Aptitude Archives

71. 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

✅ The correct answer is option B.
Total distance covered

7
+
1

miles

2
4

=
15
miles.

Time taken

hrs

4 x 75

=
1
hrs

1
x 60

min.

= 3 min.

72. 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

✅ The correct answer is option D.
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

73. 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

✅ The correct answer is option B.
Speed =

54 x
5
m/sec = 15 m/sec.

Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.

Then,
x + 300
= 15

x + 300 = 540
x = 240 m.

74. 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

✅ The correct answer is option B.
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.

75. 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

✅ The correct answer is option C.
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

76. 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

✅ The correct answer is option D.
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.

77. 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

✅ The correct answer is option B.
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

78. 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

✅ The correct answer is option A.
Formula for converting from km/hr to m/s:
X km/hr =

X x
5

m/s.

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.

79. 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

✅ The correct answer is option B.
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.

66 x
5
m/sec

55
m/sec.

Time taken to pass the man =

110 x
3
sec = 6 sec.

80. 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

✅ The correct answer is option C.
Speed =

78 x
5

m/sec
=

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.