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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.

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.

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

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

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.

81. 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

✅ The correct answer is option B.
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.

83. 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

✅ The correct answer is option C.
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

24x = 200

x =
25
.

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

50
x
18
km/hr

3
5

= 60 km/hr.

85. 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

✅ The correct answer is option C.
Relative speed = (60+ 90) km/hr

150 x
5
m/sec

125
m/sec.

Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.

Required time =

2000 x
3
sec = 48 sec.

125

87. 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

✅ The correct answer is option A.
Let the length of the first train be x metres.

Then, the length of the second train is

metres.

Relative speed = (48 + 42) kmph =

90 x
5

m/sec = 25 m/sec.

[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

600 + 3y = 1800
y = 400 m.

89. 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

✅ The correct answer is option C.
Relative speed = (40 – 20) km/hr =

20 x
5

m/sec =

m/sec.

18
9

Length of faster train =

50
x 5

m =
250
m = 27
7
m.

9
9
9

Author name: Admin