376. A and B together can complete a work in 12 days. A alone can complete in 20 days. If B does the work only half a day daily, then in how many days A and B together will complete the work ?

1. 1. 10 days

   
   
   

   2. 20 days

   
   
   

   3. 11 days

   
   
   

   4. 15 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   B’s 1 day's work
   

   =	1	-	1	=	5 - 3	=	1
   	12		20		60		30

   
   

   ∴ B's	1	day's work =	1
   	2		60

   
   ∴ (A + B)'s 1 day's work
   

   =	1	+	1	=	3 + 4	=	1
   	20		60		60		15

   
   [ ∵ B works for half day daily]
   Hence, the work will be completed in 15 days.

   Correct Option: D

   B’s 1 day's work
   

   =	1	-	1	=	5 - 3	=	1
   	12		20		60		30

   
   

   ∴ B's	1	day's work =	1
   	2		60

   
   ∴ (A + B)'s 1 day's work
   

   =	1	+	1	=	3 + 4	=	1
   	20		60		60		15

   
   [ ∵ B works for half day daily]
   Hence, the work will be completed in 15 days.

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377. A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately with A beginning, the work would be completed in

1. 1. 10	2	days
      	3

   
   
   

   2. 10	1	days
      	2

   
   
   

   3. 10	1	days
      	4

   
   
   

   4. 10	1	days
      	3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Part of work done by A and B in first two days
   

   =	1	+	1	=	4 + 3	=	7
   	9		12		36		36

   
   Part of work done in first 10 days = 35/36
   

   Remaining work = 1 -	35	=	1
   	36		36

   
   Now it is the turn of A.
   ∴ Time taken by A
   

   =	1	× 9 =	1	days
   	36		4

   
   += 10 1 4 10
   

   ∴ Total time = 10 +	1	= 10	1	days
   	4		4

   Correct Option: C

   Part of work done by A and B in first two days
   

   =	1	+	1	=	4 + 3	=	7
   	9		12		36		36

   
   Part of work done in first 10 days = 35/36
   

   Remaining work = 1 -	35	=	1
   	36		36

   
   Now it is the turn of A.
   ∴ Time taken by A
   

   =	1	× 9 =	1	days
   	36		4

   
   += 10 1 4 10
   

   ∴ Total time = 10 +	1	= 10	1	days
   	4		4

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378. A alone can complete a work in 18 days and B alone in 15 days. B alone worked at it for 10 days and then left the work. In how many more days, will A alone complete the remaining work ?

1. 1. 5 days

   
   
   

   2. 5	1	days
      	2

   
   
   

   3. 6 days

   
   
   

   4. 8 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Part of work done by B in 10 days
   

   = 10 ×	1	=	2
   	15		3

   
   

   Remaining work = 1 -	2	=	1
   	3		3

   
   

   ∴ Time taken by A =	1	× 18 = 6 days
   	3

   Correct Option: C

   Part of work done by B in 10 days
   

   = 10 ×	1	=	2
   	15		3

   
   

   Remaining work = 1 -	2	=	1
   	3		3

   
   

   ∴ Time taken by A =	1	× 18 = 6 days
   	3

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379. A can complete a piece of work in 18 days, B in 20 days and C in 30 days. B and C together start the work and are forced to leave after 2 days. The time taken by A alone to complete the remaining work is

1. 1. 10 days

   
   
   

   2. 12 days

   
   
   

   3. 15 days

   
   
   

   4. 16 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   (B + C)’s 2 days’ work
   

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

   
   

   =	1	part
   	6

   
   

   Remaining work = 1 -	1	=	5	part
   	6		6

   
   ∴ Time taken by A to complete this part of work
   

   =	5	× 18 = 15 days
   	6

   Correct Option: C

   (B + C)’s 2 days’ work
   

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

   
   

   =	1	part
   	6

   
   

   Remaining work = 1 -	1	=	5	part
   	6		6

   
   ∴ Time taken by A to complete this part of work
   

   =	5	× 18 = 15 days
   	6

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380. A and B alone can complete work in 9 days and18 days respectively. They worked together; however 3 days before the completion of the work A left. In how many days was the work completed ?

1. 1. 13 days

   
   
   

   2. 8 days

   
   
   

   3. 6 days

   
   
   

   4. 5 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the work be completed in x days.
   According to the question,
   A worked for (x –3) days, while B worked for x days.
   

   ∴	x - 3	+	x	= 1
   	9		18

   
   

   ⇒	2x - 6 + x	= 1 ⇒ 3x - 6 = 18
   	18

   
   ⇒ 3x = 18 + 6 = 24
   

   ∵ x =	24	= 8 days
   	3

   
   Aliter :
   Using Rule 8,
   Here, x = 9, y = 18, m = 3
   

   Total time taken =	(x + m)y
   	x + y

   
   

   =	(9 + 3) × 18
   	9 + 18

   
   

   =	12 × 18	= 8 days
   	27

   Correct Option: B

   Let the work be completed in x days.
   According to the question,
   A worked for (x –3) days, while B worked for x days.
   

   ∴	x - 3	+	x	= 1
   	9		18

   
   

   ⇒	2x - 6 + x	= 1 ⇒ 3x - 6 = 18
   	18

   
   ⇒ 3x = 18 + 6 = 24
   

   ∵ x =	24	= 8 days
   	3

   
   Aliter :
   Using Rule 8,
   Here, x = 9, y = 18, m = 3
   

   Total time taken =	(x + m)y
   	x + y

   
   

   =	(9 + 3) × 18
   	9 + 18

   
   

   =	12 × 18	= 8 days
   	27

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