6. An athlete runs 200 metres race in 24 seconds. His speed (in km/hr) is :

1. 1. 20

   
   
   

   2. 24

   
   
   

   3. 28.5

   
   
   

   4. 30

   
   
   

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1. View Hint View Answer Discuss in Forum

   Speed =	Distance
   	Time

   
   

   =	200	m/s
   	24

   
   

   200	m/s =	10	×	18	= 30 km/hr.
   24		24		5

   
   

   	∵   x m/s =	18	x km/hr
   		5

   Correct Option: D

   Speed =	Distance
   	Time

   
   

   =	200	m/s
   	24

   
   

   200	m/s =	10	×	18	= 30 km/hr.
   24		24		5

   
   

   	∵   x m/s =	18	x km/hr
   		5

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7. A car goes 10 metres in a second. Find its speed in km/hour.

1. 1. 40

   
   
   

   2. 32

   
   
   

   3. 48

   
   
   

   4. 36

   
   
   

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1. View Hint View Answer Discuss in Forum

   Speed of car = 10 m/sec.
   Required speed in kmph
   

   =	10 × 18	= 36 km/hr
   	5

   Correct Option: D

   Speed of car = 10 m/sec.
   Required speed in kmph
   

   =	10 × 18	= 36 km/hr
   	5

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8. A car travelling at a speed of 40 km/hour can complete a journey in 9 hours. How long will it take to travel the same distance at 60 km/hour ?

1. 1. 6 hours

   
   
   

   2. 3 hours

   
   
   

   3. 4 hours

   
   
   

   4. 4	1	hours
      	2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Total distance covered
   = Speed × Time
   = 40 × 9 = 360 km.
   The required time at 60 kmph
   

   =	360	= 6 hours.
   	60

   
   
   Second Method :
   Using Rule 9,
   Here, S₁ = 40, t₁ = 9
   S₂ = 60, t₂ = ?
   S₁t₁ = S₂t₂
   40 × 9 = 60 × t₂
   

   t2 =	4 × 9	= 6 hours.
   	6

   Correct Option: A

   Total distance covered
   = Speed × Time
   = 40 × 9 = 360 km.
   The required time at 60 kmph
   

   =	360	= 6 hours.
   	60

   
   
   Second Method :
   Using Rule 9,
   Here, S₁ = 40, t₁ = 9
   S₂ = 60, t₂ = ?
   S₁t₁ = S₂t₂
   40 × 9 = 60 × t₂
   

   t2 =	4 × 9	= 6 hours.
   	6

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9. A man travelled a certain distance by train at the rate of 25 kmph. and walked back at the
   rate of 4 kmph. If the whole journey took 5 hours 48 minutes, the distance was

1. 1. 25 km

   
   
   

   2. 30 km

   
   
   

   3. 20 km

   
   
   

   4. 15 km

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the distance be x km.
   Total time = 5 hours 48 minutes
   

   = 5 +	48	=		5 +	4		hours
   	60				5

   
   

   =	29	hours
   	5

   
   

   ∴	x	+	x	=	29
   	25		4		5

   
   

   ⇒	4x + 25x	=	29
   	100		5

   
   ⇒  5 × 29x = 29 × 100
   

   ⇒  x =	29 × 100	= 20 km.
   	5 × 29

   
   
   Second Method :
   Here, x = 25, y = 4
   

   Average speed =	2xy
   	x + y

   
   

   =	2 × 25 × 4	=	200
   	25 + 4		29

   
   

   Total Distance =	200	× 5	4
   	29		5

   
   

   =	200	×	29	= 40 km
   	29		5

   Correct Option: C

   Let the distance be x km.
   Total time = 5 hours 48 minutes
   

   = 5 +	48	=		5 +	4		hours
   	60				5

   
   

   =	29	hours
   	5

   
   

   ∴	x	+	x	=	29
   	25		4		5

   
   

   ⇒	4x + 25x	=	29
   	100		5

   
   ⇒  5 × 29x = 29 × 100
   

   ⇒  x =	29 × 100	= 20 km.
   	5 × 29

   
   
   Second Method :
   Here, x = 25, y = 4
   

   Average speed =	2xy
   	x + y

   
   

   =	2 × 25 × 4	=	200
   	25 + 4		29

   
   

   Total Distance =	200	× 5	4
   	29		5

   
   

   =	200	×	29	= 40 km
   	29		5

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10. Walking at the rate of 4 km an hour, a man covers a certain distance in 3 hours 45 minutes. If he covers the same distance on cycle, cycling at the rate of 16·5 km/hour, the time taken by him is

1. 1. 55.45 minutes

   
   
   

   2. 54.55 minutes

   
   
   

   3. 55.44 minutes

   
   
   

   4. 45.55 minutes

   
   
   

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1. View Hint View Answer Discuss in Forum

   Distance covered on foot = 4 × 3	3	km. = 15 km.
   	4

   
   ∴  Time taken on cycle
   

   =	Distance	=	15	hour
   	Speed		16.5

   
   

   =	15 × 60	minutes = 54.55 minutes
   	16.5

   Correct Option: B

   Distance covered on foot = 4 × 3	3	km. = 15 km.
   	4

   
   ∴  Time taken on cycle
   

   =	Distance	=	15	hour
   	Speed		16.5

   
   

   =	15 × 60	minutes = 54.55 minutes
   	16.5

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