21. In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hour ?

1. 1. 2.5 seconds

   
   
   

   2. 5 seconds

   
   
   

   3. 12.5 seconds

   
   
   

   4. 3	5	seconds
      	4

   
   
   

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1. View Hint View Answer Discuss in Forum

   Speed of the train
   

   = 144 kmph = 144 ×	5	= 40 m/s
   	18

   
   When a train crosses a pole, it covers a distance equal to its own length.
   

   The required time =	100
   	40

   
   

   =	5	= 2 5. seconds.
   	2

   Correct Option: A

   Speed of the train
   

   = 144 kmph = 144 ×	5	= 40 m/s
   	18

   
   When a train crosses a pole, it covers a distance equal to its own length.
   

   The required time =	100
   	40

   
   

   =	5	= 2 5. seconds.
   	2

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22. A man observed that a train 120 m long crossed him in 9 seconds. The speed (in km/hr) of the train was

1. 1. 42

   
   
   

   2. 45

   
   
   

   3. 48

   
   
   

   4. 55

   
   
   

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1. View Hint View Answer Discuss in Forum

   Speed of train
   

   =	120	×	18	= 48 kmph
   	9		5

   Correct Option: C

   Speed of train
   

   =	120	×	18	= 48 kmph
   	9		5

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23. A passenger train 150m long is travelling with a speed of 36 km/ hr. If a man is cycling in the direction of train at 9 km/hr., the time taken by the train to pass the man is

1. 1. 10 sec

   
   
   

   2. 15 sec

   
   
   

   3. 18 sec

   
   
   

   4. 20 sec

   
   
   

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1. View Hint View Answer Discuss in Forum

   Relative speed of train
   = (36 – 9) kmph = 27 kmph
   

   =	27 × 5	m/sec
   	18

   
   

   =	15	m/sec
   	2

   
   

   ∴  Required time =	Length of the train
   	Relative speed

   
   

   =	150 × 2	= 20 seconds
   	15

   Correct Option: D

   Relative speed of train
   = (36 – 9) kmph = 27 kmph
   

   =	27 × 5	m/sec
   	18

   
   

   =	15	m/sec
   	2

   
   

   ∴  Required time =	Length of the train
   	Relative speed

   
   

   =	150 × 2	= 20 seconds
   	15

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24. Buses start from a bus terminal with a speed of 20 km/hr at intervals of 10 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at intervals of 8 minutes?

1. 1. 3 km/hr

   
   
   

   2. 4 km/hr

   
   
   

   3. 5 km/hr

   
   
   

   4. 7 km/hr

   
   
   

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1. View Hint View Answer Discuss in Forum

   Distance covered in 10 minutes at 20kmph = distance covered in 8 minutes at (20 + x )
   kmph
   

   ⇒  20 ×	10	=	8	(20 + x )
   	60		60

   
   ⇒  200 = 160 + 8x
   ⇒  8x = 40
   

   ⇒  x =	40	= 5 kmph
   	8

   Correct Option: C

   Distance covered in 10 minutes at 20kmph = distance covered in 8 minutes at (20 + x )
   kmph
   

   ⇒  20 ×	10	=	8	(20 + x )
   	60		60

   
   ⇒  200 = 160 + 8x
   ⇒  8x = 40
   

   ⇒  x =	40	= 5 kmph
   	8

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25. A train, 300m long, passed a man, walking along the line in the same direction at the rate of 3 km/hr in 33 seconds. The speed of the train is

1. 1. 30 km/h

   
   
   

   2. 32 km/h

   
   
   

   3. 32	8	km/h
      	11

   
   
   

   4. 35	8	km/h
      	11

   
   
   

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1. View Hint View Answer Discuss in Forum

   If the speed of the train be x kmph, then relative speed = (x – 3) kmph.
   

   or (x – 3) ×	5	m/sec
   	18

   
   

   ∴	300					= 33
   	(x − 3) ×	5
   		18

   
   ⇒  5400 = 33 × 5 (x – 3)
   ⇒  360 = 11 (x – 3)
   ⇒  11x – 33 = 360
   

   ⇒  x =	393	= 35	8	kmph
   	11		11

   Correct Option: D

   If the speed of the train be x kmph, then relative speed = (x – 3) kmph.
   

   or (x – 3) ×	5	m/sec
   	18

   
   

   ∴	300					= 33
   	(x − 3) ×	5
   		18

   
   ⇒  5400 = 33 × 5 (x – 3)
   ⇒  360 = 11 (x – 3)
   ⇒  11x – 33 = 360
   

   ⇒  x =	393	= 35	8	kmph
   	11		11

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