346. 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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347. 45 men can complete a work in 16 days. Four days after they started working, 36 more men joined them. How many days will they now take to complete the remaining work ?

1. 1. 6 days

   
   
   

   2. 8 days

   
   
   

   3. 6	2	days
      	3

   
   
   

   4. 7	3	days
      	4

   
   
   

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1. View Hint View Answer Discuss in Forum

   45 men’s 4 days’ work =	1
   	4

   
   Remaining work
   

   = 1 -	1	=	3
   	4		4

   
   

   	M1D1	=	M2D2
   	W1		W2

   
   

   	45 × 16	=	81 × D2
   	1		3/4

   
   

   ⇒ D2 =	45 × 16	= 6	2	days
   	27 × 4		3

   
   Aliter : Using Rule 10,
   Here, A = 45, a = 16
   b = 4, B = 36
   Required days
   

   =	A(a - b)	days
   	(A + B)

   
   

   =	45(16 - 4)
   	(45 + 36)

   
   

   =	45 × 12
   	81

   
   

   =	20	= 6	2	days
   	3		3

   Correct Option: C

   45 men’s 4 days’ work =	1
   	4

   
   Remaining work
   

   = 1 -	1	=	3
   	4		4

   
   

   	M1D1	=	M2D2
   	W1		W2

   
   

   	45 × 16	=	81 × D2
   	1		3/4

   
   

   ⇒ D2 =	45 × 16	= 6	2	days
   	27 × 4		3

   
   Aliter : Using Rule 10,
   Here, A = 45, a = 16
   b = 4, B = 36
   Required days
   

   =	A(a - b)	days
   	(A + B)

   
   

   =	45(16 - 4)
   	(45 + 36)

   
   

   =	45 × 12
   	81

   
   

   =	20	= 6	2	days
   	3		3

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348. 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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349. 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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350. A and B can separately complete a piece of work in 20 days and 30 days respectively. They worked together for some time, then B left the work. If A completed the rest of the work in 10 days, then B worked for

1. 1. 6 days

   
   
   

   2. 8 days

   
   
   

   3. 12 days

   
   
   

   4. 16 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let A and B worked together for x days
   According to the question,
   Part of work done by A for (x + 10) days + part of work done by B for x days = 1
   

   ⇒	x + 10	+	x	= 1
   	20		30

   
   

   ⇒	3x + 30 + 2x	= 1
   	60

   
   ⇒ 5x + 30 = 60
   ⇒ 5x = 30
   

   ⇒	30	= 6 days
   	5

   
   Aliter :
   Using Rule 20,
   Here, m =20, n= 30,
   π = x and time taken by A alone = 10
   mn p m n n - + ()
   

   ⇒ 10 =	mn - p(m + n)
   	n

   
   

   10 =	30 × 20 - x(30 + 20)
   	30

   
   = 600 – x 50
   50x = 300 x = 6
   ⇒ B worked for 6 days

   Correct Option: A

   Let A and B worked together for x days
   According to the question,
   Part of work done by A for (x + 10) days + part of work done by B for x days = 1
   

   ⇒	x + 10	+	x	= 1
   	20		30

   
   

   ⇒	3x + 30 + 2x	= 1
   	60

   
   ⇒ 5x + 30 = 60
   ⇒ 5x = 30
   

   ⇒	30	= 6 days
   	5

   
   Aliter :
   Using Rule 20,
   Here, m =20, n= 30,
   π = x and time taken by A alone = 10
   mn p m n n - + ()
   

   ⇒ 10 =	mn - p(m + n)
   	n

   
   

   10 =	30 × 20 - x(30 + 20)
   	30

   
   = 600 – x 50
   50x = 300 x = 6
   ⇒ B worked for 6 days

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