26. 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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27. 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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28. A train passes two persons walking in the same direction at a speed of 3 km/hour and 5km/hour respectively in 10 seconds and 11 seconds respectively. The speed of the train is

1. 1. 28 km/hour

   
   
   

   2. 27 km/hour

   
   
   

   3. 25 km/hour

   
   
   

   4. 24 km/hour

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the speed of train be x kmph and its length be y km.
   When the train crosses a man, it covers its own length
   According to he question,
   

   =	y					= 10
   	(x − 3) ×	5
   		3

   
   ⇒  18 y = 10 × 5(x –3)
   ⇒  18y = 50x –150   ..... (i)
   

   and,	y					= 11
   	(x − 5) ×	5
   		18

   
   ⇒  18y = 55(x–5)
   ⇒  18y = 55x –275   .... (ii)
   From equations (i) and (ii),
   55x –275 = 50x–150
   ⇒  55x –50x = 275 – 150
   ⇒  5x = 125
   

   ⇒  x =	125	= 25
   	5

   
   ∴  Speed of the train = 25 kmph
   Second Method :
   Here, S₁ = 3, S₂ = 5
   

   t1 =	10	,  t2 =	11
   	3600		3600

   
   

   Speed of train =	t1S1 − t2S2
   	t1 − t2

   
   

   =	3 × 10	−	5 × 11
   	3600		3600
   	10	−	11
   	3600		3600

   
   

   =	− 25	×	3600
   	3600		− 1

   
   = 25 m/sec

   Correct Option: C

   Let the speed of train be x kmph and its length be y km.
   When the train crosses a man, it covers its own length
   According to he question,
   

   =	y					= 10
   	(x − 3) ×	5
   		3

   
   ⇒  18 y = 10 × 5(x –3)
   ⇒  18y = 50x –150   ..... (i)
   

   and,	y					= 11
   	(x − 5) ×	5
   		18

   
   ⇒  18y = 55(x–5)
   ⇒  18y = 55x –275   .... (ii)
   From equations (i) and (ii),
   55x –275 = 50x–150
   ⇒  55x –50x = 275 – 150
   ⇒  5x = 125
   

   ⇒  x =	125	= 25
   	5

   
   ∴  Speed of the train = 25 kmph
   Second Method :
   Here, S₁ = 3, S₂ = 5
   

   t1 =	10	,  t2 =	11
   	3600		3600

   
   

   Speed of train =	t1S1 − t2S2
   	t1 − t2

   
   

   =	3 × 10	−	5 × 11
   	3600		3600
   	10	−	11
   	3600		3600

   
   

   =	− 25	×	3600
   	3600		− 1

   
   = 25 m/sec

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29. If a train, with a speed of 60 km/ hr, crosses a pole in 30 seconds, the length of the train (in metres) is :

1. 1. 1000

   
   
   

   2. 900

   
   
   

   3. 750

   
   
   

   4. 500

   
   
   

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1. View Hint View Answer Discuss in Forum

   Speed of train = 60 kmph
   

   = 60 ×	5	×	50	m/sec
   	18		3

   
   &there4:  Length of train
   = Speed × Time
   

   =	50	× 30 = 500 m
   	3

   Correct Option: D

   Speed of train = 60 kmph
   

   = 60 ×	5	×	50	m/sec
   	18		3

   
   &there4:  Length of train
   = Speed × Time
   

   =	50	× 30 = 500 m
   	3

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30. 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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