406. A man travels a distance of 24 km at 6 kmph. Another distance of 24 km at 8 kmph and a third distance of 24 km at 12 kmph. His average speed for the whole journey (in kmph) is

1. 1. 8	2
      	3

   
   
   

   2. 8

   
   
   

   3. 2	10
      	13

   
   
   

   4. 9

   
   
   

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1. View Hint View Answer Discuss in Forum

   Total distance
   = 24 + 24 + 24 = 72 km.
   

   Total time =		24	+	24	+	24		hours
   		6		8		12

   
   = (4 + 3 + 2) hours = 9 hours
   

   ∴ Required average speed =	Total distance
   	Total time

   
   

   =	72	= 8 kmph.
   	9

   Correct Option: B

   Total distance
   = 24 + 24 + 24 = 72 km.
   

   Total time =		24	+	24	+	24		hours
   		6		8		12

   
   = (4 + 3 + 2) hours = 9 hours
   

   ∴ Required average speed =	Total distance
   	Total time

   
   

   =	72	= 8 kmph.
   	9

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407. A constant distance from Chennai to Bangalore is covered by Express train at 100 km/hr. If it returns to the same distance at 80 km/hr, then the average speed during the whole journey is

1. 1. 90.20 km/hr

   
   
   

   2. 88.78 km/hr

   
   
   

   3. 88.98 km/hr

   
   
   

   4. 88.89 km/hr

   
   
   

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1. View Hint View Answer Discuss in Forum

   If same distance are covered at two different speed of x and y kmph, the average speed of journey
   

   =	2xy
   	x + y

   
   

   =		2 × 100 × 80		kmph
   		100 + 80

   
   = 88.89 kmph

   Correct Option: D

   If same distance are covered at two different speed of x and y kmph, the average speed of journey
   

   =	2xy
   	x + y

   
   

   =		2 × 100 × 80		kmph
   		100 + 80

   
   = 88.89 kmph

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408. A person went from A to B at an average speed of x km/hr and returned from B to A at an average speed of y km/hr. What was his average speed during the total journey ?

1. 1. x + y

      2xy

   
   
   

   2. 2xy

      x + y

   
   
   

   3. 2

      x + y

   
   
   

   4. 1	+	1
      x		y

   
   
   

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1. View Hint View Answer Discuss in Forum

   Required average speed =		2xy		kmph
   		x + y

   
   [Since, can be given as corollary If the distance between A and B be z units, then
   

   Average speed =	Total distance
   	Time taken

   
   

   =	z + z
   	z	+	z
   	x		y

   
   

   =	2
   	1	+	1
   	x		y

   
   

   =	2
   	x + y
   	xy

   
   

   =	2xy
   	x + y

   Correct Option: B

   Required average speed =		2xy		kmph
   		x + y

   
   [Since, can be given as corollary If the distance between A and B be z units, then
   

   Average speed =	Total distance
   	Time taken

   
   

   =	z + z
   	z	+	z
   	x		y

   
   

   =	2
   	1	+	1
   	x		y

   
   

   =	2
   	x + y
   	xy

   
   

   =	2xy
   	x + y

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409. A man travels 50 km at speed 25 km/h and next 40 km at 20 km/h and there after travels 90 km at 15 km/h. His average speed is :

1. 1. 18 kmph.

   
   
   

   2. 25 kmph.

   
   
   

   3. 20 kmph.

   
   
   

   4. 15 kmph.

   
   
   

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1. View Hint View Answer Discuss in Forum

   Total distance covered
   = (50 + 40 + 90) km
   = 180 km
   

   Time =	Distance
   	Speed

   
   

   ∴   Total time taken =		50	+	40	+	90		hours
   		25		20		15

   
   = (2 + 2 + 6) hours
   = 10 hours
   

   ∴  Average speed =	Total distance
   	Total time taken

   
   

   =	180	= 18 kmph
   	10

   Correct Option: A

   Total distance covered
   = (50 + 40 + 90) km
   = 180 km
   

   Time =	Distance
   	Speed

   
   

   ∴   Total time taken =		50	+	40	+	90		hours
   		25		20		15

   
   = (2 + 2 + 6) hours
   = 10 hours
   

   ∴  Average speed =	Total distance
   	Total time taken

   
   

   =	180	= 18 kmph
   	10

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410. A man goes from a place A to B at a speed of 12 km/hr and returns from B to A at a speed of 18 km/hr. The average speed for the whole journey is

1. 1. 14	2	km/hr
      	5

   
   
   

   2. 15 km/hr

   
   
   

   3. 15	1	km/hr
      	2

   
   
   

   4. 16 km/hr

   
   
   

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1. View Hint View Answer Discuss in Forum

   Average speed =		2xy		kmph
   		x + y

   
   

   =		2 × 12 × 18		kmph
   		12 + 18

   
   

   =		2 × 12 × 18		kmph
   		30

   
   

   = 14	2	kmph
   	5

   Correct Option: B

   Average speed =		2xy		kmph
   		x + y

   
   

   =		2 × 12 × 18		kmph
   		12 + 18

   
   

   =		2 × 12 × 18		kmph
   		30

   
   

   = 14	2	kmph
   	5

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