1. A can finish a work in 7 days. B can finish the same work in 9 days. The number days required to finish the same work by both of them together is

1. 1. 1	15
      	16

   
   
   

   2. 2	15
      	16

   
   
   

   3. 3	15
      	16

   
   
   

   4. 4	15
      	16

   
   
   

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1. View Hint View Answer Discuss in Forum

   A’s 1 day’s work =	1
   	7

   
   

   B’s 1 day’s work =	1
   	9

   
   ∴ (A + B)’s 1 day’s work
   

   =	1	+	1
   	7		9

   
   

   =	1440	=	40	= 3	1	days
   	468		13		13

   
   

   ∴ Required time =	63	days
   	16

   
   

   = 3	15	days
   	16

   Correct Option: C

   A’s 1 day’s work =	1
   	7

   
   

   B’s 1 day’s work =	1
   	9

   
   ∴ (A + B)’s 1 day’s work
   

   =	1	+	1
   	7		9

   
   

   =	1440	=	40	= 3	1	days
   	468		13		13

   
   

   ∴ Required time =	63	days
   	16

   
   

   = 3	15	days
   	16

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2. A, B and C working separately can do a piece of work in 11 days, 20 days and 55 days respectively. In how many days, the work will be completed if A is assisted by B and C on alternate days ?

1. 1. 2

   
   
   

   2. 6

   
   
   

   3. 4

   
   
   

   4. 8

   
   
   

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1. View Hint View Answer Discuss in Forum

   (A + B)’s 1 day’s work
   

   =	1	+	1
   	11		20

   
   

   =	20 + 11	=	31
   	220		220

   
   (A + C)’s 1 day’s work
   

   =	1	+	1
   	11		55

   
   

   =	5 + 1	=	6
   	55		55

   
   Work done in first two days
   

   =	31	+	6
   	220		55

   
   

   =	31 + 24	=	55	=	1
   	220		220		4

   
   ∴ Required time = 2 × 4 = 8 days

   Correct Option: D

   (A + B)’s 1 day’s work
   

   =	1	+	1
   	11		20

   
   

   =	20 + 11	=	31
   	220		220

   
   (A + C)’s 1 day’s work
   

   =	1	+	1
   	11		55

   
   

   =	5 + 1	=	6
   	55		55

   
   Work done in first two days
   

   =	31	+	6
   	220		55

   
   

   =	31 + 24	=	55	=	1
   	220		220		4

   
   ∴ Required time = 2 × 4 = 8 days

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3. A can do a piece of work in 12 days and B in 24 days. If they work together, in how many days will they finish the work?

1. 1. 12 days

   
   
   

   2. 20 days

   
   
   

   3. 15 days

   
   
   

   4. 8 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   (A + B)’s 1 day’s work
   

   =	1	+	1
   	12		24

   
   

   =	2 + 1	=	3	=	1
   	24		24		8

   
   ∴ Required time = 8 days

   Correct Option: D

   (A + B)’s 1 day’s work
   

   =	1	+	1
   	12		24

   
   

   =	2 + 1	=	3	=	1
   	24		24		8

   
   ∴ Required time = 8 days

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4. A and B together can finish a job in 24 days, while A, B and C together can finish the same job in 8 days. C alone will finish the job in

1. 1. 12 days

   
   
   

   2. 14 days

   
   
   

   3. 16 days

   
   
   

   4. 24 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   (A + B)’s 1 day’s work =	1
   	24

   
   

   (A + B + C)’s 1 day’s work =	1
   	6

   
   

   ∴ C’s 1 day’s work =	1	-	1
   	8		24

   
   

   =	3 - 1	=	2	=	1
   	24		24		12

   
   ∴ Required time = 12 days

   Correct Option: A

   (A + B)’s 1 day’s work =	1
   	24

   
   

   (A + B + C)’s 1 day’s work =	1
   	6

   
   

   ∴ C’s 1 day’s work =	1	-	1
   	8		24

   
   

   =	3 - 1	=	2	=	1
   	24		24		12

   
   ∴ Required time = 12 days

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5. A and B together can do a piece of work in 6 days and A alone can do it in 9 days. The number of days B will take to do it alone is

1. 1. 18 days

   
   
   

   2. 24 days

   
   
   

   3. 9 days

   
   
   

   4. 12 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   (A + B)’s 1 day’s work =	1
   	6

   
   

   A’s 1 day’s work =	1
   	9

   
   

   ∴ B’s 1 day’s work =	1	-	1
   	6		9

   
   

   =	3 - 2	=	1
   	18		18

   
   ∴ Required time = 18 days

   Correct Option: A

   (A + B)’s 1 day’s work =	1
   	6

   
   

   A’s 1 day’s work =	1
   	9

   
   

   ∴ B’s 1 day’s work =	1	-	1
   	6		9

   
   

   =	3 - 2	=	1
   	18		18

   
   ∴ Required time = 18 days

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