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31. Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:

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Solution:
LetusnamethetrainsasAandB.Then,(A'sspeed):(B'sspeed)=b:a=16:9=4:3
32. A 100 m long train is going at a speed of 60 km/hr. It will cross a 140 m long railway bridge in-

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Solution:
Speed  = (60×518)m/sec = 503 m/secTotal distance covered = (100 + 140) m = 240 m∴Required time = (240×350)sec = 725sec = 14.4 sec
33. A train 132 m long passes a telegraph pole in 6 seconds. Find the speed of the train?

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Solution:
Speed = (1326)m/sec = (22×185)km/sec = 79.2 km/hr
34. A train running at the speed of 60 kmph crosses a 200 m long platform in 27 seconds. What is the length of the train?

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Solution:
Speed = (60×518)m/sec = 503m/secTime = 27 sec.Let the length of the train be x metres.Then,x+20027 = 503 ⇔x+200=(503×27)=450⇔x=450−200=250 metres
35. A train running at a speed of 90 km/hr crosses a platform double its length in 36 seconds. What is the length of the platform in meters?

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Solution:
Let the length of the train be x metres.Then, length of the platform = (2x) metres.Speed of the train = (90×518)m/sec=25m/sec∴x+2x25=36⇒3x=900⇒x=300Hence, length of platform = 2x=(2×300)m=600m
36. A train of length 150 meters takes 40.5 seconds to cross a tunnel of length 300 meters. What is the speed of the train in km/hr?

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Solution:
Speed = (150+30040.5)m/sec=(45040.5×185)km/hr=40km/hr
37. A 280 meter long train crosses a platform thrice its length in 50 seconds. What is the speed of the train in km/hr?

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Solution:
Length of train = 280 m Length of platform = (3×280) m = 840m∴Speed of train = (280+84050)m/sec=112050m/sec=(112050×185)km/hr=80.64km/hr
38. A train 110 meters 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?

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Solution:
Speed of train relative to man = (60+6)km/hr=66km/hr=(66×518)m/sec=(553)m/sec∴Time taken to pass the man=(110×355)sec=6sec
39. Two trains A and B start running together from the same point in the same direction, at the speed of 60 kmph and 72 kmph respectively. If the length of each of the trains is 240 meters, how long will it take for B to cross train A?

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Solution:
Relative speed = (72−60) km/hr = 12 km/hr=(12×518)m/sec=(103)m/secTotal distance covered = Sum of lengths of trains = (240 + 240) m = 480 mTime taken = (480×310)sec=144sec=2min24sec
40. 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 second is?

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Solution:
Relative speed = (60 + 90) km/hr = (150×518)m/sec = (1253)m/secDistance coverd = (1.10 + 0.9)km = 2 km = 2000 mRequired time = (2000×3125)sec=48 sec

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