411. A alone can do a piece of work in 20 days and B alone in 30 days. They begin to work together. They will finish half of the work in :

1. 1. 8 days

   
   
   

   2. 9 days

   
   
   

   3. 12 days

   
   
   

   4. 6 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   (A+B)’s 1 day’s work
   

   =	1	+	1	=	3 + 2	=	1
   	20		30		60		12

   
   ∴ Work done in 6 days
   

   =	6	=	1
   	12		2

   
   Aliter : Using basics of Rule 2,
   Here, x = 20, y = 30
   They do the work in
   

   =	xy	days
   	x + y

   
   

   =	20 × 30	= 12 days
   	20 + 30

   
   Half of the work they do in 6 days

   Correct Option: D

   (A+B)’s 1 day’s work
   

   =	1	+	1	=	3 + 2	=	1
   	20		30		60		12

   
   ∴ Work done in 6 days
   

   =	6	=	1
   	12		2

   
   Aliter : Using basics of Rule 2,
   Here, x = 20, y = 30
   They do the work in
   

   =	xy	days
   	x + y

   
   

   =	20 × 30	= 12 days
   	20 + 30

   
   Half of the work they do in 6 days

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412. A can do a work in 20 days and B in 40 days. If they work on it together for 5 days, then the fraction of the work that is left is :

1. 1. 5

      8

   
   
   

   2. 8

      15

   
   
   

   3. 7

      15

   
   
   

   4. 1

      10

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using basics of Rule 2,
   (A + B)’s 5 days’ work
   

   = 5		1	+	1
   		20		40

   
   

   = 5		2 + 1
   		40

   
   

   =	15	=	3
   	40		8

   
   

   ∴ Remaining work = 1 -	3	=	5
   	8		8

   Correct Option: A

   Using basics of Rule 2,
   (A + B)’s 5 days’ work
   

   = 5		1	+	1
   		20		40

   
   

   = 5		2 + 1
   		40

   
   

   =	15	=	3
   	40		8

   
   

   ∴ Remaining work = 1 -	3	=	5
   	8		8

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413. A is twice as good a workman as B and together they finish a piece of work in 14 days. The number of days taken by A alone to finish the work is

1. 1. 11 days

   
   
   

   2. 21 days

   
   
   

   3. 28 days

   
   
   

   4. 42 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 2,
   If A completes the work in x days, B will take 2x days.
   

   ∴	1	+	1	=	1
   	x		2x		14

   
   

   =	2 + 1	=	1
   	2x		14

   
   ⇒ 2x = 42 ⇒ x = 21 days
   

   Correct Option: B

   Using Rule 2,
   If A completes the work in x days, B will take 2x days.
   

   ∴	1	+	1	=	1
   	x		2x		14

   
   

   =	2 + 1	=	1
   	2x		14

   
   ⇒ 2x = 42 ⇒ x = 21 days
   

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414. Sunil completes a work in 4 days, whereas Dinesh completes the work in 6 days. Ramesh works
     

     1	1
     	2

     times as fast as Sunil. The three together can complete the work in

1. 1. 1	5	days
      	12

   
   
   

   2. 1	5	days
      	7

   
   
   

   3. 1	3	days
      	8

   
   
   

   4. 1	5	days
      	19

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 3,
   Time taken by Ramesh
   

   = 4 ×	2	=	8	days
   	3		3

   
   Work done by all three in 1 day
   

   	1	+	1	+	3
   	4		6		8

   
   ∴ Required time
   

   =	24	= 1	5	days
   	19		19

   Correct Option: D

   Using Rule 3,
   Time taken by Ramesh
   

   = 4 ×	2	=	8	days
   	3		3

   
   Work done by all three in 1 day
   

   	1	+	1	+	3
   	4		6		8

   
   ∴ Required time
   

   =	24	= 1	5	days
   	19		19

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415. Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3 as efficiently as he actually did, the work would have been completed in 3 days. To complete the job alone, A would require

1. 1. 5	1	days
      	5

   
   
   

   2. 6	1	days
      	4

   
   
   

   3. 7	1	days
      	2

   
   
   

   4. 8	3	days
      	4

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 2,
   If A alone does the work in x days and B alone does the work in y days, then
   

   	1	+	1	=	1	...........(i)
   	x		y		5

   
   

   Again,	2	+	1	=	1	...........(ii)
   	x		3y		3

   
   By equation (ii) × 3 – (i),
   

   ⇒	6	+	1	-	1	-	1	= 1 -	1
   	x		y		x		y		5

   
   

   	6	-	1	=	4
   	x		x		5

   
   

   =	6 - 1	=	4
   	x		5

   
   

   ⇒ x =	25	= 6	1	days
   	4		4

   Correct Option: B

   Using Rule 2,
   If A alone does the work in x days and B alone does the work in y days, then
   

   	1	+	1	=	1	...........(i)
   	x		y		5

   
   

   Again,	2	+	1	=	1	...........(ii)
   	x		3y		3

   
   By equation (ii) × 3 – (i),
   

   ⇒	6	+	1	-	1	-	1	= 1 -	1
   	x		y		x		y		5

   
   

   	6	-	1	=	4
   	x		x		5

   
   

   =	6 - 1	=	4
   	x		5

   
   

   ⇒ x =	25	= 6	1	days
   	4		4

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