356. A moving train passes a platform 50 metre long in 14 seconds and a lamp post in 10 seconds. The speed of the train (in km/h) is :

1. 1. 24

   
   
   

   2. 36

   
   
   

   3. 40

   
   
   

   4. 45

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the length of train be x metre.
   When a train crosses a platform, distance covered by it = length of train and platform.
   

   ∴  Speed of train =	x + 50	=	x
   	14		10

   
   

   ⇒	x + 50	=	x
   	7		5

   
   ⇒  7x = 5x + 250
   ⇒  7x – 5x = 250
   

   ⇒ 2x = 250 ⇒ x =	250	= 125 metre
   	2

   
   

   ∴ Speed of train =	x
   	10

   
   

   =		125		m./sec.
   		10

   
   

   =		125	×	18		kmph
   		10		5

   
   = 45 kmph

   Correct Option: D

   Let the length of train be x metre.
   When a train crosses a platform, distance covered by it = length of train and platform.
   

   ∴  Speed of train =	x + 50	=	x
   	14		10

   
   

   ⇒	x + 50	=	x
   	7		5

   
   ⇒  7x = 5x + 250
   ⇒  7x – 5x = 250
   

   ⇒ 2x = 250 ⇒ x =	250	= 125 metre
   	2

   
   

   ∴ Speed of train =	x
   	10

   
   

   =		125		m./sec.
   		10

   
   

   =		125	×	18		kmph
   		10		5

   
   = 45 kmph

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357. A train 270 metres long is running at a speed of 36 km per hour, then it will cross a bridge of
     length 180 metres in :

1. 1. 40 sec

   
   
   

   2. 45 sec

   
   
   

   3. 50 sec

   
   
   

   4. 35 sec

   
   
   

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1. View Hint View Answer Discuss in Forum

   36 kmph =		36 ×	5		m/sec.
   			18

   
   = 10 m/sec.
   

   Required time =	270 + 180
   	10

   
   = 45 seconds

   Correct Option: B

   36 kmph =		36 ×	5		m/sec.
   			18

   
   = 10 m/sec.
   

   Required time =	270 + 180
   	10

   
   = 45 seconds

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358. A train, 500 metre long, running at a uniform speed, passes a station in 35 seconds. If the length of the platform is 221 metre, the speed of the train in km/hr is
     

1. 1. 72	1
      	35

   
   
   

   2. 74.16

   
   
   

   3. 24.76

   
   
   

   4. 78.54

   
   
   

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1. View Hint View Answer Discuss in Forum

   Speed of train =	Length of platform and train
   	Time taken in crossing

   
   

   =		221 + 500		metre/second
   		35

   
   

   =		721		metre/second
   		35

   
   

   =		721 × 18		kmph
   		35 × 5

   
   = 74.16 kmph

   Correct Option: B

   Speed of train =	Length of platform and train
   	Time taken in crossing

   
   

   =		221 + 500		metre/second
   		35

   
   

   =		721		metre/second
   		35

   
   

   =		721 × 18		kmph
   		35 × 5

   
   = 74.16 kmph

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359. A train, 200 metre long, is running at a speed of 54 km/hr. The time in seconds that will be taken by train to cross a 175 metre long bridge is :

1. 1. 12.5

   
   
   

   2. 20

   
   
   

   3. 25

   
   
   

   4. 10

   
   
   

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1. View Hint View Answer Discuss in Forum

   Speed of train = 54 kmph
   

   =		54 × 5		m/sec.
   		18

   
   = 15 m/sec.
   

   ∴  Required time =	Length of train and bridge
   	Speed of train

   
   

   =		200 + 175		seconds
   		15

   
   

   =		375		seconds
   		15

   
   = 25 seconds

   Correct Option: C

   Speed of train = 54 kmph
   

   =		54 × 5		m/sec.
   		18

   
   = 15 m/sec.
   

   ∴  Required time =	Length of train and bridge
   	Speed of train

   
   

   =		200 + 175		seconds
   		15

   
   

   =		375		seconds
   		15

   
   = 25 seconds

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360. A train 180 m long moving at the speed of 20 m/sec. over-takes a man moving at a speed of 10m/sec in the same direction. The train passes the man in :

1. 1. 6 sec

   
   
   

   2. 9 sec

   
   
   

   3. 18 sec

   
   
   

   4. 27 sec

   
   
   

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1. View Hint View Answer Discuss in Forum

   Relative speed of man and train = 20 – 10 = 10m/sec.
   

   ∴  Required time =	180	= 18 seconds
   	10

   Correct Option: C

   Relative speed of man and train = 20 – 10 = 10m/sec.
   

   ∴  Required time =	180	= 18 seconds
   	10

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