391. A train travelled at a speed of 35 km/hr for the first 10 minutes and at a speed of 20 km/hr for the next 5 minutes. The average speed of the train for the total 15 minutes is

1. 1. 30 km/hr

   
   
   

   2. 23 km/hr

   
   
   

   3. 31 km/hr

   
   
   

   4. 29 km/hr

   
   
   

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1. View Hint View Answer Discuss in Forum

   Distance covered =		35 ×	10	+ 20 ×	5		km
   			60		60

   
   

   =		35	+	10		km
   		6		6

   
   

   =	45	km
   	6

   
   Total time = 15 minutes
   

   =	1	hour
   	4

   
   

   ∴  Required average speed =	Distance covered
   	Time taken

   
   

   =	45	× 4
   	6

   
   = 30 kmph

   Correct Option: A

   Distance covered =		35 ×	10	+ 20 ×	5		km
   			60		60

   
   

   =		35	+	10		km
   		6		6

   
   

   =	45	km
   	6

   
   Total time = 15 minutes
   

   =	1	hour
   	4

   
   

   ∴  Required average speed =	Distance covered
   	Time taken

   
   

   =	45	× 4
   	6

   
   = 30 kmph

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392. When Alisha goes by car at 50 kmph, she reaches her office 5 minutes late. But when she takes her motorbike, she reaches 3 minutes early. If her office is 25 kms away, what is the approximate average speed at which she rides her motorbike ?

1. 1. 68 kmph

   
   
   

   2. 62 kmph

   
   
   

   3. 58 kmph

   
   
   

   4. 52 kmph

   
   
   

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1. View Hint View Answer Discuss in Forum

   Difference of time = 5 + 3 = 8 minutes
   

   =	8	hour =	2	hour
   	60		15

   
   If the speed of motorbike be x kmph, then
   

   25	−	25	=	2
   50		x		15

   
   

   ⇒	25	=	1	−	2
   	x		2		15

   
   

   ⇒	25	=	15 − 4	=	11
   	x		30		30

   
   ⇒ 11x = 25 × 30
   

   ⇒ x =	25 × 30
   	11

   
   

   =	750	= 68.18 kmph
   	11

   
   ≈ 68 kmph

   Correct Option: A

   Difference of time = 5 + 3 = 8 minutes
   

   =	8	hour =	2	hour
   	60		15

   
   If the speed of motorbike be x kmph, then
   

   25	−	25	=	2
   50		x		15

   
   

   ⇒	25	=	1	−	2
   	x		2		15

   
   

   ⇒	25	=	15 − 4	=	11
   	x		30		30

   
   ⇒ 11x = 25 × 30
   

   ⇒ x =	25 × 30
   	11

   
   

   =	750	= 68.18 kmph
   	11

   
   ≈ 68 kmph

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393. A man goes to a place on bicycle at speed of 16 km/hr and comes back at lower speed. If the average speed is 6.4 km/hr in total journey, then the return speed (in km/hr) is :

1. 1. 10

   
   
   

   2. 8

   
   
   

   3. 6

   
   
   

   4. 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the speed of cyclist while returning be x kmph.
   

   ∴  Average speed =	2 × 16 × x
   	16 + x

   
   

   ⇒  6.4 =	32x
   	16 + x

   
   ⇒  6.4 × 16 + 6.4x = 32x
   ⇒  32x – 6.4x = 6.4 × 16
   ⇒  25.6x = 6.4 × 16
   

   ⇒  x =	6.4 × 16
   	25.6

   
   = 4 kmph.

   Correct Option: D

   Let the speed of cyclist while returning be x kmph.
   

   ∴  Average speed =	2 × 16 × x
   	16 + x

   
   

   ⇒  6.4 =	32x
   	16 + x

   
   ⇒  6.4 × 16 + 6.4x = 32x
   ⇒  32x – 6.4x = 6.4 × 16
   ⇒  25.6x = 6.4 × 16
   

   ⇒  x =	6.4 × 16
   	25.6

   
   = 4 kmph.

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394. A car completed a journey of 400 km in 12	1	hrs.
     	2

     The first	3	th of the journey was done at 30 km/hr.
     	4

     Calculate the speed for the rest of the journey.

1. 1. 45 km/hr

   
   
   

   2. 25 km/hr

   
   
   

   3. 40 km/hr

   
   
   

   4. 30 km/hr

   
   
   

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1. View Hint View Answer Discuss in Forum

   Total distance covered = 400 km.
   

   Total time =	25	hours
   	2

   
   

   ∴	3	th of total journey
   	4

   
   

   =	3	× 400 = 300 km.
   	4

   
   

   Time taken =	Distance
   	Speed

   
   

   =	300	= 10 hours
   	30

   
   

   Remaining time =	25	− 2
   	2

   
   

   =	25 − 20	=	5	hours
   	2		2

   
   Remaining distance = 100 km.
   

   ∴  Required speed of car =	100
   	5
   	2

   
   

   =	100 × 2	= 40 kmph.
   	5

   Correct Option: C

   Total distance covered = 400 km.
   

   Total time =	25	hours
   	2

   
   

   ∴	3	th of total journey
   	4

   
   

   =	3	× 400 = 300 km.
   	4

   
   

   Time taken =	Distance
   	Speed

   
   

   =	300	= 10 hours
   	30

   
   

   Remaining time =	25	− 2
   	2

   
   

   =	25 − 20	=	5	hours
   	2		2

   
   Remaining distance = 100 km.
   

   ∴  Required speed of car =	100
   	5
   	2

   
   

   =	100 × 2	= 40 kmph.
   	5

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395. Durga walks 5 km from her home to school in 60 minutes, then bicycles back to home along the same route at 15 km per hour. Her sister Smriti makes the same round trip, but does so at half of Durga’s average speed. How much time does Smriti spend on her round trip ?

1. 1. 120 minutes

   
   
   

   2. 40 minutes

   
   
   

   3. 160 minutes

   
   
   

   4. 80 minutes

   
   
   

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1. View Hint View Answer Discuss in Forum

   Durga’s average speed =		2xy		kmph.
   		x + y

   =		2 × 5 × 15		kmph
   		20

   
   

   =	15	kmph
   	2

   
   Distance of School = 5 km.
   

   ∴  Required time = 2		5		hours
   		15/4

   
   

   =		2 × 5 × 4		hours
   		15

   
   

   =	8	hours
   	3

   
   

   =		8	× 60		minutes
   		3

   
   = 160 minutes

   Correct Option: C

   Durga’s average speed =		2xy		kmph.
   		x + y

   =		2 × 5 × 15		kmph
   		20

   
   

   =	15	kmph
   	2

   
   Distance of School = 5 km.
   

   ∴  Required time = 2		5		hours
   		15/4

   
   

   =		2 × 5 × 4		hours
   		15

   
   

   =	8	hours
   	3

   
   

   =		8	× 60		minutes
   		3

   
   = 160 minutes

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