56. A train running at	7	its own speed reached a place
    	11

    in 22 hours. How much time could be saved if the train would run at its own speed?

1. 1. 14 hours

   
   
   

   2. 7 hours

   
   
   

   3. 8 hours

   
   
   

   4. 16 hours

   
   
   

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1. View Hint View Answer Discuss in Forum

   Since the train runs at 7/11 of its own speed, the time it takes is 11/7 of its usual speed.
   Let the usual time taken be t hours.
   

   Then we can write,	11	t = 22
   	7

   
   

   ∴ t =	22 × 7	= 14 hours
   	11

   
   Hence, time saved
   = 22 – 14 = 8 hours

   Correct Option: C

   Since the train runs at 7/11 of its own speed, the time it takes is 11/7 of its usual speed.
   Let the usual time taken be t hours.
   

   Then we can write,	11	t = 22
   	7

   
   

   ∴ t =	22 × 7	= 14 hours
   	11

   
   Hence, time saved
   = 22 – 14 = 8 hours

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57. A man with	3	of his usual speed reaches
    	5

    the destination 2	1	hours late.
    	2

    Find his usual time to reach the destination.

1. 1. 4 hours

   
   
   

   2. 3 hours

   
   
   

   3. 3	3	hours
      	4

   
   
   

   4. 4	1	hours
      	2

   
   
   

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1. View Hint View Answer Discuss in Forum

   3/5 of usual speed will take 5/3 of usual time.
   [∵  time & speed are inversely proportional]
   

   ∴	5	of usual time
   	3

   
   

   = usual time +	5
   	2

   
   

   ⇒	2	of usual time =	5	⇒ usual time
   	3		2

   
   

   =	5	×	3	=	15	= 3	3	hours.
   	2		2		4		4

   
   Second Method :
   

   Here, A = 3, B = 5, t = 2	1
   	2

   
   

   Usual time =	A	× time
   	Diff. of A and B

   
   

   =	3	× 2	1
   	5 − 3		2

   
   

   =	3	×	5
   	2		2

   
   

   =	15	= 3	3	hours
   	4		4

   Correct Option: C

   3/5 of usual speed will take 5/3 of usual time.
   [∵  time & speed are inversely proportional]
   

   ∴	5	of usual time
   	3

   
   

   = usual time +	5
   	2

   
   

   ⇒	2	of usual time =	5	⇒ usual time
   	3		2

   
   

   =	5	×	3	=	15	= 3	3	hours.
   	2		2		4		4

   
   Second Method :
   

   Here, A = 3, B = 5, t = 2	1
   	2

   
   

   Usual time =	A	× time
   	Diff. of A and B

   
   

   =	3	× 2	1
   	5 − 3		2

   
   

   =	3	×	5
   	2		2

   
   

   =	15	= 3	3	hours
   	4		4

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58. A car travelling with	5	of its usual speed covers
    	7

    42 km in 1 hour 40 min 48 sec. What is the usual speed of the car?

1. 1. 17	6	km/hr
      	7

   
   
   

   2. 35 km/hr

   
   
   

   3. 25 km/hr

   
   
   

   4. 30 km/hr

   
   
   

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1. View Hint View Answer Discuss in Forum

   1 hr 40 min 48 sec
   

   = 1 hr		40 +	48		min
   			60

   
   

   = 1 hr		40 +	4		min
   			5

   
   

   = 1 hr	204	min
   	5

   
   

   =		1 +	204		hr
   			300

   
   

   =	504	hr
   	300

   
   

   ∴  Speed =	42
   	504
   	300

   
   = 25 kmph
   

   Now,	5	×usual speed = 25
   	7

   
   

   ∴  Usual speed =	25 × 7
   	5

   
   = 35 kmph

   Correct Option: B

   1 hr 40 min 48 sec
   

   = 1 hr		40 +	48		min
   			60

   
   

   = 1 hr		40 +	4		min
   			5

   
   

   = 1 hr	204	min
   	5

   
   

   =		1 +	204		hr
   			300

   
   

   =	504	hr
   	300

   
   

   ∴  Speed =	42
   	504
   	300

   
   = 25 kmph
   

   Now,	5	×usual speed = 25
   	7

   
   

   ∴  Usual speed =	25 × 7
   	5

   
   = 35 kmph

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59. Walking at three-fourth of his usual speed, a man covers a certain distance in 2 hours more than the time he takes to cover the distance at his usual speed. The time taken by him to cover the distance with his usual speed is

1. 1. 4.5 hours

   
   
   

   2. 5.5 hours

   
   
   

   3. 6 hours

   
   
   

   4. 5 hours

   
   
   

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1. View Hint View Answer Discuss in Forum

   4	×usual time – usual time = 2
   3

   
   

   ⇒	1	usual time = 2
   	3

   
   ∴  Usual time = 2 × 3 = 6 hours
   Second Method :
   

   Here,	A	=	3	, time= 2 hrs.
   	B		4

   
   

   Usual time =	A	× time
   	Diff. of A and B

   
   

   =	3	× 2 = 6 hours
   	(4 − 3)

   Correct Option: C

   4	×usual time – usual time = 2
   3

   
   

   ⇒	1	usual time = 2
   	3

   
   ∴  Usual time = 2 × 3 = 6 hours
   Second Method :
   

   Here,	A	=	3	, time= 2 hrs.
   	B		4

   
   

   Usual time =	A	× time
   	Diff. of A and B

   
   

   =	3	× 2 = 6 hours
   	(4 − 3)

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60. By walking at	3	of his usual speed,
    	4

    a man reaches his office 20 minutes later than his usual time. The usual time taken by him to reach his office is

1. 1. 75 minutes

   
   
   

   2. 60 minutes

   
   
   

   3. 40 minutes

   
   
   

   4. 30 minutes

   
   
   

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1. View Hint View Answer Discuss in Forum

   4	of usual time = Usual time + 20 minutes
   3

   
   

   ∴	1	of usual time = 20 minutes
   	3

   
   ⇒  Usual time = 20 × 3
   = 60 minutes
   Second Method :
   Here, A = 3, B= 4, t = 20 minutes
   

   Usual time taken =	A	× time
   	Diff. of A and B

   
   

   =	3	× 20 = 60 minutes
   	(4 − 3)

   Correct Option: B

   4	of usual time = Usual time + 20 minutes
   3

   
   

   ∴	1	of usual time = 20 minutes
   	3

   
   ⇒  Usual time = 20 × 3
   = 60 minutes
   Second Method :
   Here, A = 3, B= 4, t = 20 minutes
   

   Usual time taken =	A	× time
   	Diff. of A and B

   
   

   =	3	× 20 = 60 minutes
   	(4 − 3)

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