86. A speed of 45 km per hour is the same as

1. 1. 12.5 metre/seccond

   
   
   

   2. 13 metre/seccond

   
   
   

   3. 15 metre/seccond

   
   
   

   4. 12 metre/seccond

   
   
   

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1. View Hint View Answer Discuss in Forum

   Speed = 45 kmph
   

   =		45 × 1000		metre/second
   		60 × 60

   
   

   =		45 × 5		metre/second
   		18

   
   = 12.5 metre/second

   Correct Option: A

   Speed = 45 kmph
   

   =		45 × 1000		metre/second
   		60 × 60

   
   

   =		45 × 5		metre/second
   		18

   
   = 12.5 metre/second

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87. If I walk at 5 km/hour, I miss a train by 7 minutes. If, however, I walk at 6 km/hour, I reach the station 5 minutes before the departure of the train. The distance (in km) between my house and the station is

1. 1. 6

   
   
   

   2. 5

   
   
   

   3. 4

   
   
   

   4. 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the required distance be x km, then
   

   x	−	x	=	12	=	1
   5		6		60		5

   
   

   ⇒	6x − 5x	=	1	⇒	x	=	1
   	30		5		30		5

   
   ⇒  x = 6 km.

   Correct Option: A

   Let the required distance be x km, then
   

   x	−	x	=	12	=	1
   5		6		60		5

   
   

   ⇒	6x − 5x	=	1	⇒	x	=	1
   	30		5		30		5

   
   ⇒  x = 6 km.

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88. A man has to be at a certain place at a certain time. He finds that he shall be 20 minutes late if he walks at 3 km/hour speed and 10 minutes earlier if he walks at a speed of 4 km/hour . The distance he has to walk is

1. 1. 24 km

   
   
   

   2. 12·5 km

   
   
   

   3. 10 km

   
   
   

   4. 6 km

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the required distance be x km.
   

   ∴	x	−	x	=	30
   	3		4		60

   
   

   ⇒	x	=	1	⇒ x =	1	× 12 = 6 km
   	12		2		2

   Correct Option: D

   Let the required distance be x km.
   

   ∴	x	−	x	=	30
   	3		4		60

   
   

   ⇒	x	=	1	⇒ x =	1	× 12 = 6 km
   	12		2		2

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89. Ravi travels 300 km partly by train and partly by car. He takes 4 hours to reach, if he travels 60 km by train and rest by car. He will take 10 minutes more if he were to travel 100 km by train and rest by car. The speed of the train is :

1. 1. 50 km/hr

   
   
   

   2. 60 km/hr

   
   
   

   3. 100 km/hr

   
   
   

   4. 120 km/hr

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the speed of train be x kmph and that of car be y kmph,
   then
   

   60	+	240	= 4   ...(i)
   x		y

   
   

   and,	100	+	200	=	25
   	x		y		6

   
   

   ⇒	4	+	8	=	1	...(ii)
   	x		y		6

   
   By equation (i ) – equation (ii) × 30
   

   60	+	240	−	120	−	240	= 4 – 5
   x		y		x		y

   
   

   ⇒  −	60	= − 1
   	x

   
   ⇒  x = 60 kmph

   Correct Option: B

   Let the speed of train be x kmph and that of car be y kmph,
   then
   

   60	+	240	= 4   ...(i)
   x		y

   
   

   and,	100	+	200	=	25
   	x		y		6

   
   

   ⇒	4	+	8	=	1	...(ii)
   	x		y		6

   
   By equation (i ) – equation (ii) × 30
   

   60	+	240	−	120	−	240	= 4 – 5
   x		y		x		y

   
   

   ⇒  −	60	= − 1
   	x

   
   ⇒  x = 60 kmph

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90. A is twice as fast runner as B, and B is thrice as fast runner as C. If C travelled a distance in 1 hour 54 minutes, the time taken by B to cover the same distance is

1. 1. 19 minutes

   
   
   

   2. 38 minutes

   
   
   

   3. 51 minutes

   
   
   

   4. 57 minutes

   
   
   

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1. View Hint View Answer Discuss in Forum

   Ratio of the speed of A and B
   = A : B = 2 : 1 = 6 : 3
   B : C = 3 : 1
   ∴  A : B : C = 6 : 3 : 1
   ∴  Ratio of their time taken
   

   =	1	:	1	: 1 = 1 : 2 : 6
   	6		3

   
   

   ∴  Time taken by B =		2	× 114		minutes
   		6

   
   = 38 minutes

   Correct Option: B

   Ratio of the speed of A and B
   = A : B = 2 : 1 = 6 : 3
   B : C = 3 : 1
   ∴  A : B : C = 6 : 3 : 1
   ∴  Ratio of their time taken
   

   =	1	:	1	: 1 = 1 : 2 : 6
   	6		3

   
   

   ∴  Time taken by B =		2	× 114		minutes
   		6

   
   = 38 minutes

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