What is the time taken by a 180 m long train running at 54 kmph to cross a man standing on a platform?

Q.1

A train 100 m long is running at the speed of 30 km / hr. Find the time taken by it to pass a man standing near the railway line.

36 sec

20 sec

12 sec

10 sec

1. Explanation :

   Speed of the train = (30 * 5/18) m / sec = (25/3) m/ sec. Distance moved in passing the standing man = 100 m. Required time taken = 100/(25/3) = (100 *(3/25)) sec = 12 sec

Q.2

A train is moving at a speed of 132 km/br. If the length of the train is 110 metres, how long will it take to cross a railway platform 165 metres long?

8 sec

12 ½ sec

10 sec

7 ½ sec

1. Explanation :

   Speed of train = 132 *(5/18) m/sec = 110/3 m/sec. Distance covered in passing the platform = (110 + 165) m = 275 m.
   Time taken =275 *(3/110) sec =15/2 sec = 7 ½ sec

Q.3

A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed?

58 km

53 km

60 km

54 km

1. Explanation :

   Let the length of the train be x metres, Then, the train covers x metres in 8 seconds and (x + 180) metres in 20 sec \(\frac{x}{8}\) = \(\frac{(x+180)}{20}\) 20x = 8(x + 180) ---> x = 120.

   Length of the train = 120 m. Speed of the train = (120/8) m / sec = m / sec = (15 *18/5) kmph = 54 km

Q.4

A train 150 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?

18 sec

10 sec

9 sec

14 sec

1. Explanation :

   Speed of the train relative to man = (68 - 8) kmph = (60* 5/18) m/sec = (50/3)m/sec

   Time taken by the train to cross the man = Time taken by It to cover 150 m at 50/3 m / sec = 150 *3/ 50 sec = 9sec

Q.5

A train 220 m long is running with a speed of 59 kmph.. In what will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going?

15 sec

9 sec

12 sec

8 sec

1. Explanation :

   Speed of the train relative to man = (59 + 7) kmph = 66 *5/18 m/sec = 55/3 m/sec. Time taken by the train to cross the man = Time taken by it to cover 220 m

   at (55/3) m / sec = (220 *3/55) sec = 12 sec

Q.6

Two trains 137 metres and 163 metres in length are running towards each other on parallel lines, one at the rate of 42 kmph and another at 48 kmpb. In what time will they be clear of each other from the moment they meet?

12 sec

20 sec

25 sec

18 sec

1. Explanation :

   Relative speed of the trains = (42 + 48) kmph = 90 kmph =(90*5/18) m / sec = 25 m /sec.
   Time taken by the trains to'pass each other = Time taken to cover (137 + 163) m at 25 m /sec =(300/25) sec = 12 sec

Q.7

Two trains 100 metres and 120 metres long are running in the same direction with speeds of 72 km/hr,In howmuch time will the first train cross the second?

18 sec

36 sec

44 sec

12 sec

1. Explanation :

   Relative speed of the trains = (72 - 54) km/hr = 18 km/hr = (18 * 5/18) m/sec = 5 m/sec. Time taken by the trains to cross each other = Time taken to cover (100 + 120) m at 5 m /sec = (220/5) sec = 44 sec.

Q.8

A train 100 metres long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train.?

48 kmhr

40 kmhr

60 kmph

55 kmph

1. Explanation :

   Let the speed of the train be x kmph. Speed of the train relative to man = (x + 5) kmph = (x + 5) * 5/18 m/sec.

   Therefore 100/((x+5)*5/18)=6 <=> 30 (x + 5) = 1800 <=> x = 55 Speed of the train is 55 kmph.

Q.9

A train running at 54 kmph takes 20 seconds to pass a platform. Next it takes.12 sec to pass a man walking at 6 kmph in the same direction in which the train is going . Find the length of the train and the length of the platform.

100,120

160,140

180,120

110,150

1. Explanation :

   Let the length of train be x metres and length of platform be y metres. Speed of the train relative to man = (54 - 6) kmph = 48 kmph = 48*(5/18) m/sec = 40/3 m/sec. In passing a man, the train covers its own length with relative speed. Length of train = (Relative speed * Time) = ( 40/3)*12 m = 160 m. Also, speed of the train = 54 *(5/18)m / sec = 15 m / sec.

   (x+y)/15 = 20 <=> x + y = 300 <=> Y = (300 - 160) m = 140 m.
   

Q.10

A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?

48 kmph

86 kmph

62 kmph

67 kmph

1. Explanation :

   Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph. Speed of goods train = (112 - 50) kmph = 62 kmph.

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