171. If a train runs at 70 km/hour, it reaches its destination late by 12 minutes. But if it runs at 80 km/ hour, it is late by 3 minutes. The correct time to cover the journey is

1. 1. 58 minutes

   
   
   

   2. 2 hours

   
   
   

   3. 1 hour

   
   
   

   4. 59 minutes

   
   
   

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1. View Hint View Answer Discuss in Forum

   Distance of journey = x km
   Difference of time = 12 – 3 = 9 minutes
   

   =	9	hour =	3	hour
   	60		20

   
   

   ∴	x	−	x	=	3
   	70		80		20

   
   

   ⇒	x	−	x	=	3
   	7		8		2

   
   

   ⇒	8x − 7x	=	3
   	56		2

   
   

   ⇒	x	=	3
   	56		2

   
   

   ⇒  x =	3	× 56 = 84 km
   	2

   
   ∴   Required correct time
   

   =	84	hours – 12 minutes
   	70

   
   

   =		84	× 60 − 12		minutes
   		70

   
   = 72 – 12 = 60 minutes
   = 1 hour

   Correct Option: C

   Distance of journey = x km
   Difference of time = 12 – 3 = 9 minutes
   

   =	9	hour =	3	hour
   	60		20

   
   

   ∴	x	−	x	=	3
   	70		80		20

   
   

   ⇒	x	−	x	=	3
   	7		8		2

   
   

   ⇒	8x − 7x	=	3
   	56		2

   
   

   ⇒	x	=	3
   	56		2

   
   

   ⇒  x =	3	× 56 = 84 km
   	2

   
   ∴   Required correct time
   

   =	84	hours – 12 minutes
   	70

   
   

   =		84	× 60 − 12		minutes
   		70

   
   = 72 – 12 = 60 minutes
   = 1 hour

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172. A train passes a 50 metres long platform in 14 seconds and a man standing on the platform in 10 seconds.The speed of the train is :

1. 1. 24 km/hr

   
   
   

   2. 36 km/hr

   
   
   

   3. 40 km/hr

   
   
   

   4. 45 km/hr

   
   
   

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1. View Hint View Answer Discuss in Forum

   Rule 10 and Rule 1,
   Let the length of train be x metres
   ∴  According to question
   

   Speed of the train =	x	m/sec.
   	10

   
   Also, the speed of the train

   =		x + 50		m/sec.
   		14

   
   [∵  It passes the platform in 14 seconds]
   Both the speeds should be equal,
   i.e.,
   

   x	=	x + 50
   10		14

   
   or 14x = 10x + 500
   or 14x – 10x = 500
   or 4x = 500
   ∴  x = 125 metres
   

   Hence, Speed =	125	= 12 5. m/sec.
   	10

   
   

   =	12.5 × 18	km/hr.
   	5

   
   = 45 km/hr.

   Correct Option: D

   Rule 10 and Rule 1,
   Let the length of train be x metres
   ∴  According to question
   

   Speed of the train =	x	m/sec.
   	10

   
   Also, the speed of the train

   =		x + 50		m/sec.
   		14

   
   [∵  It passes the platform in 14 seconds]
   Both the speeds should be equal,
   i.e.,
   

   x	=	x + 50
   10		14

   
   or 14x = 10x + 500
   or 14x – 10x = 500
   or 4x = 500
   ∴  x = 125 metres
   

   Hence, Speed =	125	= 12 5. m/sec.
   	10

   
   

   =	12.5 × 18	km/hr.
   	5

   
   = 45 km/hr.

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173. A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 264 metres long in 20 seconds. The length of the train (in metres) is :

1. 1. 188

   
   
   

   2. 176

   
   
   

   3. 175

   
   
   

   4. 96

   
   
   

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1. View Hint View Answer Discuss in Forum

   Rule 10 and Rule 1,
   Let length of train be x m
   

   ∴   Speed of train =	x + 264
   	20

   
   

   Also, speed of train =	x
   	8

   
   

   Obviously,	x	=	x + 264
   	8		20

   
   

   ⇒	x	=	x + 264
   	2		5

   
   ⇒  5x = 2x + 528
   ⇒  5x – 2x = 528
   ⇒  x = 528 ÷ 3 = 176 m

   Correct Option: B

   Rule 10 and Rule 1,
   Let length of train be x m
   

   ∴   Speed of train =	x + 264
   	20

   
   

   Also, speed of train =	x
   	8

   
   

   Obviously,	x	=	x + 264
   	8		20

   
   

   ⇒	x	=	x + 264
   	2		5

   
   ⇒  5x = 2x + 528
   ⇒  5x – 2x = 528
   ⇒  x = 528 ÷ 3 = 176 m

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174. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train ?

1. 1. 69.5 km/hr

   
   
   

   2. 70 km/hr

   
   
   

   3. 79 km/hr

   
   
   

   4. 79.2 km/hr

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the length of train be x metres.
   Then, speed of train when it
   

   passes a telegraph post =	x	m/sec.
   	8

   
   and speed of train, when it
   

   passes the bridge =	x + 264
   	20

   
   Clearly,
   

   x	=	x + 264
   8		20

   
   

   ⇒	x	=	x + 264
   	2		5

   
   ⇒  5x = 2x + 528
   ⇒  3x = 528
   

   ⇒  x =	528	= 176m
   	3

   
   

   ∴   Speed of train =	176	= 22 m/sec.
   	8

   
   

   = 22 ×	18	Kmph
   	5

   
   = 79.2 kmph

   Correct Option: D

   Let the length of train be x metres.
   Then, speed of train when it
   

   passes a telegraph post =	x	m/sec.
   	8

   
   and speed of train, when it
   

   passes the bridge =	x + 264
   	20

   
   Clearly,
   

   x	=	x + 264
   8		20

   
   

   ⇒	x	=	x + 264
   	2		5

   
   ⇒  5x = 2x + 528
   ⇒  3x = 528
   

   ⇒  x =	528	= 176m
   	3

   
   

   ∴   Speed of train =	176	= 22 m/sec.
   	8

   
   

   = 22 ×	18	Kmph
   	5

   
   = 79.2 kmph

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175. A person standing on a railway platform noticed that a train took 21 seconds to completely pass through the platform which was 84 m long and it took 9 seconds in passing him. The speed of the train was

1. 1. 25.2 km/hour

   
   
   

   2. 32.4 km/hour

   
   
   

   3. 50.4 km/hour

   
   
   

   4. 75.6 km/hour

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the length of train be x metres.
   When the train crosses the standing man,
   

   its speed =	x
   	9

   
   When the train crosses the platform of length 84 m, its speed
   

   =	x + 84
   	21

   
   

   Obviously,	x	=	x + 84
   	9		21

   
   ⇒  21x – 9x = 9 × 84
   ⇒  12x = 9 × 84
   

   ⇒  x =	9 × 84	= 63 m
   	12

   
   

   ∴   Required speed =	63	m/sec
   	9

   
   

   =	63	×	18	kmph = 25.2 kmph
   	9		5

   Correct Option: A

   Let the length of train be x metres.
   When the train crosses the standing man,
   

   its speed =	x
   	9

   
   When the train crosses the platform of length 84 m, its speed
   

   =	x + 84
   	21

   
   

   Obviously,	x	=	x + 84
   	9		21

   
   ⇒  21x – 9x = 9 × 84
   ⇒  12x = 9 × 84
   

   ⇒  x =	9 × 84	= 63 m
   	12

   
   

   ∴   Required speed =	63	m/sec
   	9

   
   

   =	63	×	18	kmph = 25.2 kmph
   	9		5

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