236. Ronald and Elan are working on an Assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take working together on two different computers to type an assignment of 110 pages ?

1. 1. 7 hrs. 30 min.

   
   
   

   2. 8 hrs.

   
   
   

   3. 8 hrs. 15 min.

   
   
   

   4. 8 hrs. 25 min.

   
   
   

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1. View Hint View Answer Discuss in Forum

   Ronald’s 1 hour’s work =	32	=	16	pages
   	6		3

   
   [ Pages typed in 6 hrs. = 32
   

   ∴ pages typed in 1 hr =	32	]
   	6

   
   Elan’s 1 hour’s work = 8 pages 1 hour’s work of the both
   

   =	16	+ 8 =	40	pages
   	3		3

   
   

   Correct Option: C

   Ronald’s 1 hour’s work =	32	=	16	pages
   	6		3

   
   [ Pages typed in 6 hrs. = 32
   

   ∴ pages typed in 1 hr =	32	]
   	6

   
   Elan’s 1 hour’s work = 8 pages 1 hour’s work of the both
   

   =	16	+ 8 =	40	pages
   	3		3

   
   

   ∴ Required time =	110 × 3	=	33	hours
   	40		4

   
   Required time = 8 hours 15 minutes

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237. A can do a piece of work in 20 days and B can do the same piece of work in 30 days. Find in how many days both can do the work ?

1. 1. 16 days

   
   
   

   2. 14 days

   
   
   

   3. 10 days

   
   
   

   4. 12 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   A ’s 1day’s work =	1
   	20

   
   

   B ’s 1day’s work =	1
   	30

   
   

   ∴ (A + B)’s 1 day’s work =	1	+	1
   	20		30

   
   

   (A + B)’s 1 day’s work =	3 + 2	+	1
   	60		12

   
   Hence, the work will be completed in 12 days. When worked together.
   Second method to solve this question ,
   

   Time taken =	xy	days
   	x + y

   
   

   Correct Option: D

   A ’s 1day’s work =	1
   	20

   
   

   B ’s 1day’s work =	1
   	30

   
   

   ∴ (A + B)’s 1 day’s work =	1	+	1
   	20		30

   
   

   (A + B)’s 1 day’s work =	3 + 2	+	1
   	60		12

   
   Hence, the work will be completed in 12 days. When worked together.
   Second method to solve this question ,
   

   Time taken =	xy	days
   	x + y

   
   

   Time taken =	20 × 30	days
   	20 + 30

   
   

   Time taken =	600	= 12 days
   	50

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238. A can do as much work as B and C together can do. A and B can together do a piece of work in 9 hours 36 minutes and C can do it in 48 hours. The time (in hours) that B needs to do the work alone, is :

1. 1. 18 hrs

   
   
   

   2. 24 hrs

   
   
   

   3. 30 hrs

   
   
   

   4. 12 hrs

   
   
   

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1. View Hint View Answer Discuss in Forum

   9 hours 36 minutes = 9 +	36	= 9	3	hours
   	60		5

   
   

   9 hours 36 minutes =	48	hours
   	5

   
   

   (A + B)’s 1 hour’s work =	5
   	48

   
   

   C’s 1 hour’s work =	1
   	48

   
   

   (A + B + C)’s 1 hour’s work =	5	+	1	=	1	.......(i)
   	48		48		8

   
   A’s 1 hours work = (B + C)’s 1 hour’s work .....(ii)
   From equations (i) and (ii),
   

   2 × (A’s 1 hour’s work) =	1
   	8

   
   

   A’s 1 hour’s work =	1
   	16

   
   

   ∴ B’s 1 hour’s work =	5	-	1
   	48		16

   
   

   Correct Option: B

   9 hours 36 minutes = 9 +	36	= 9	3	hours
   	60		5

   
   

   9 hours 36 minutes =	48	hours
   	5

   
   

   (A + B)’s 1 hour’s work =	5
   	48

   
   

   C’s 1 hour’s work =	1
   	48

   
   

   (A + B + C)’s 1 hour’s work =	5	+	1	=	1	.......(i)
   	48		48		8

   
   A’s 1 hours work = (B + C)’s 1 hour’s work .....(ii)
   From equations (i) and (ii),
   

   2 × (A’s 1 hour’s work) =	1
   	8

   
   

   A’s 1 hour’s work =	1
   	16

   
   

   ∴ B’s 1 hour’s work =	5	-	1
   	48		16

   
   

   B’s 1 hour’s work =	5 - 3	=	1
   	48		24

   
   ∴ B alone will finish the work in 24 hours

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239. A can do a piece of work in 12 days and B in 15 days. They work together for 5 days and then B left. The days taken by A to finish the remaining work is

1. 1. 3

   
   
   

   2. 5

   
   
   

   3. 10

   
   
   

   4. 12l

   
   
   

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1. View Hint View Answer Discuss in Forum

   Work done by A and B in 5 days = 5		1	+	1		= 5		5 + 4
   		12		15				60

   
   

   Work done by A and B in 5 days = 5 ×	9	=	9	=	3
   	60		12		4

   
   

   Remaining work = 1 -	3	=	1
   	4		4

   
   

   ∴ Time taken by A =	1	× 12 = 3 days.
   	4

   
   Second method to solve this question ,
   Here, m = 12, n = 15,p = 5
   

   Correct Option: A

   Work done by A and B in 5 days = 5		1	+	1		= 5		5 + 4
   		12		15				60

   
   

   Work done by A and B in 5 days = 5 ×	9	=	9	=	3
   	60		12		4

   
   

   Remaining work = 1 -	3	=	1
   	4		4

   
   

   ∴ Time taken by A =	1	× 12 = 3 days.
   	4

   
   Second method to solve this question ,
   Here, m = 12, n = 15,p = 5
   

   Time taken by A =	mn - p (m + n)	days
   	n

   
   

   Time taken by A =	12 × 15 - 5(12 + 15)
   	15

   
   

   Time taken by A =	180 - 135	= 3 days
   	15

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240. A and B together can dig a trench in 12 days, which A alone can dig in 28 days; B alone can dig it in

1. 1. 20 days

   
   
   

   2. 21 days

   
   
   

   3. 22 days

   
   
   

   4. 23 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   B’s 1 day’s work = (A + B)’s 1 day’s work – A’s 1 day’s work
   

   B’s 1 day’s work =	1	-	1	=	7 - 3
   	12		28		84

   
   

   B’s 1 day’s work =	4	=	1
   	84		21

   
   ∴ Required time = 21 days
   Second method to solve this question ,
   

   Correct Option: B

   B’s 1 day’s work = (A + B)’s 1 day’s work – A’s 1 day’s work
   

   B’s 1 day’s work =	1	-	1	=	7 - 3
   	12		28		84

   
   

   B’s 1 day’s work =	4	=	1
   	84		21

   
   ∴ Required time = 21 days
   Second method to solve this question ,
   

   Time taken by B =	xy	days
   	x - y

   
   

   Time taken by B =	12 × 28
   	28 - 12

   
   

   Time taken by B =	12 × 28	= 21 days
   	16

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