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71. A man sitting in a train is counting the pillars of electricity. The distance between two pillars is 60 meters, and the speed of the train is 42 km/hr. In 5 hours, how many pillars will he count?

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Solution:
Distance covered by the train in 5 hours
= (42 × 5) km
= 210 km
= 210000 m
∴ Number of pillars counted by the man
= (21000060+1)
= 3500 + 1
= 3501
72. A 120 meter long train is running at a speed of 90 km/hr. It will cross a railway platform 230 m long in :

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Solution:
Speed = (90×518)   m/sec = 25 m/sec
Total distance covered
= (120 + 230) m
= 350 m
∴ Required time
= 35025 seconds
= 14 seconds
73. A 50 meter long train passes over a bridge at the speed of 30 km per hour. If it takes 36 seconds to cross the bridge, what is the length of the bridge?

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Solution:
Speed = (30×518)  m/sec = 253 m/sec
Time = 36 second
Let the length of the bridge be x meters.
Then, 50+x36   = 253
⇒ 3(50 + x) = 900
⇒ 50 + x = 300
⇒ x = 250 meters
74. A train takes 5 minutes to cross a telegraphic post. Then the time taken by another train whose length is just double of the first train and moving with same speed to cross a platform of its own length is :

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Solution:
Let the length of the train be x metres.
Time taken to cover x meters = 5 min
= (5 × 60) sec
= 300 sec
Speed of the train = x300 m/sec
Length of the second train = 2x meters
Length of the platform = 2x meters
∴ Required time
=[2x+2x(x300)]sec=(4x×300x)sec=1200sec=120060min=20minutes
75. 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?

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Solution:
Speed = (54×518)  m/sec = 15 m/sec
Length of the train = (15 × 20) m = 300 m
Let the length of the platform be x meters
Then, x+30036  = 15
⇒ x + 300 = 540
⇒ x = 240 meters
76. A train speeds past a pole in 20 seconds and speeds past a platform 100 meters in length in 30 seconds. What is the length of the train?

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Solution:
Let the length of the train be x meters and its speed be y m/sec.
Then, xy = 20
⇒ y = x20
∴ x+10030  = x20
⇒ 30x = 20x + 2000
⇒ 10x = 2000
⇒ x = 200 meters
77. The time taken by a train 180 m long, travelling at 42 kmph, in passing a person walking in the same direction at 6 kmph, will be

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Solution:
Speed of train relative to man
= (42 - 6) kmph = 36 kmph
= (36×518)  m/sec
= 10 m/sec
∴ Time taken to pass the man
= 18010 sec
= 18 sec
78. Two trains 200 meters and 150 meters long are running on parallel rails in the same direction at speed of 40 km/hr and 45 km/hr respectively. Time taken by the faster train to cross the slowed train will be:

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Solution:
Relative speed = (45 - 40) km/hr = 5 km/hr
= (5×518)  m/sec
= 2518 m/sec
Total distance covered = Sum of lengths of trains = (200 + 150) m = 350 m
∴ Time taken
= (350×1825)   sec
= 252 seconds
79. A train with 90 km/hr crosses a bridge in 36 seconds. Another train 100 meters shorter crosses the same bridge at 45 km/hr. What is the time taken by the second train to cross the bridge?

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Solution:
Let the lengths of the train and the bridge be x meters and y meters respectively.
Speed of the first train
= 90 km/hr
= (90×518)  m/sec
= 25 m/sec
Speed of the second train= 45 km/hr
= (45×518)  m/sec
= 252 m/sec
Then, x+y36 = 25
⇒ x + y = 900
∴ Required time
=[(x−100)+y252]sec=[(x+y)−100252]sec=(800×225)sec=64sec
80. A train 125 m long passes a man, running at 5 kmph in the same direction in which the train is going, in 10 seconds. The speed of the train is:

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Solution:
Speed of the train relative to man
=12510m/sec=252m/sec=(252×185)m/sec=45km/hr
Let the speed of the train be x kmph.
Then, relative speed = (x - 5) kmph
∴ x - 5 = 45 or
x = 50 km/hr

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