81. A contractor undertook to complete a project in 90 days and employed 60 men on it. After 60 days, he found that 3/4 of the work has already been completed. How many men can he discharge so that the project may be completed exactly on time ?

1. 1. 40

   
   
   

   2. 20

   
   
   

   3. 30

   
   
   

   4. 15

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using basics of Rule 1,
   
   

   ⇒ 30 ×	3	× x = 60 ×	1	× 60
   	4		4

   
   

   ⇒ x =	60 × 60	= 40
   	30 × 3

   
   ∴ 20 men should be discharged.

   Correct Option: B

   Using basics of Rule 1,
   
   

   ⇒ 30 ×	3	× x = 60 ×	1	× 60
   	4		4

   
   

   ⇒ x =	60 × 60	= 40
   	30 × 3

   
   ∴ 20 men should be discharged.

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82. A can complete 2/3 of a work in 4 days and B can complete 3/5 of the work in 6 days. In how many days can both A and B together complete the work ?

1. 1. 3

   
   
   

   2. 2

   
   
   

   3. 3	3
      	4

   
   
   

   4. 2	7
      	8

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using basics of Rule 2,
   Time taken by A to complete the work
   

   =	4 × 3	= 6 days
   	2

   
   Time taken by B to complete the work
   

   =	6 × 5	= 10 days
   	3

   
   ∴ (A + B)’s 1 day’s work
   

   =	1	+	1	=	5 + 3	=	4
   	6		10		30		15

   
   ∴ A and B together will complete the work in
   

   	15	= 3	3	days.
   	4		4

   Correct Option: C

   Using basics of Rule 2,
   Time taken by A to complete the work
   

   =	4 × 3	= 6 days
   	2

   
   Time taken by B to complete the work
   

   =	6 × 5	= 10 days
   	3

   
   ∴ (A + B)’s 1 day’s work
   

   =	1	+	1	=	5 + 3	=	4
   	6		10		30		15

   
   ∴ A and B together will complete the work in
   

   	15	= 3	3	days.
   	4		4

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83. A can complete 1/3 of a work in 5 days and B, 2/5 of the work in 10 days. In how many days both A and B together can complete the work ?

1. 1. 10 days

   
   
   

   2. 9	3	days
      	8

   
   
   

   3. 8	4	days
      	5

   
   
   

   4. 7	1	days
      	2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using basics of Rule 2,
   Time taken by A alone in doing the work = 15 days
   Time taken by B alone in doing the work
   

   =	10 × 5	= 25 days
   	2

   
   ∴ (A + B)’s 1 day’s work
   

   =	1	+	1	=	5 + 3	=	8
   	15		25		75		75

   
   ∴ Hence, the work will be completed in
   

   	75	= 9	3	days.
   	8		8

   Correct Option: B

   Using basics of Rule 2,
   Time taken by A alone in doing the work = 15 days
   Time taken by B alone in doing the work
   

   =	10 × 5	= 25 days
   	2

   
   ∴ (A + B)’s 1 day’s work
   

   =	1	+	1	=	5 + 3	=	8
   	15		25		75		75

   
   ∴ Hence, the work will be completed in
   

   	75	= 9	3	days.
   	8		8

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84. If 28 men complete 7/8 of a piece of work in a week, then the number of men, who must be engaged to get the remaining work completed in another week, is

1. 1. 5

   
   
   

   2. 6

   
   
   

   3. 4

   
   
   

   4. 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using basics of Rule 1,
   
   

   =	7	:	1	:: 28 : x
   	8		8

   
   where x is no. of men
   

   ⇒	7	× x	1	× 28
   	8		8

   
   

   ⇒ x =	28 × 8	= 4
   	7 × 8

   Correct Option: C

   Using basics of Rule 1,
   
   

   =	7	:	1	:: 28 : x
   	8		8

   
   where x is no. of men
   

   ⇒	7	× x	1	× 28
   	8		8

   
   

   ⇒ x =	28 × 8	= 4
   	7 × 8

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85. A can do 1/2 of a piece of work in 5 days, B can do 3/5 of the same work in 9 days and C can do 2/3 of that work in 8 days. In how many days can three of them together do the work ?

1. 1. 3 days

   
   
   

   2. 5 days

   
   
   

   3. 4	1	days
      	2

   
   
   

   4. 4 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using basics of Rule 3,
   

   A can do	1	work in 5 days.
   	2

   
   ∴ A can do 1 work in 10 days
   Similarly,
   

   B can do 1 work in	5	× 9 = 15 days
   	3

   
   

   C can do 1 work in 8 ×	3	= 12 days.
   	2

   
   Now,
   

   A’s 1 day’s work =	1
   	10

   
   

   B’s 1 day’s work =	1
   	15

   
   

   C’s 1 day’s work =	1
   	12

   
   ∴ (A + B + C)’s 1 day’s work
   

   =	1	+	1	+	1
   	10		15		12

   
   

   =	6 + 4 + 5	=	15	=	1
   	60		60		4

   
   Hence, (A + B + C) together can complete the work in 4 days.

   Correct Option: D

   Using basics of Rule 3,
   

   A can do	1	work in 5 days.
   	2

   
   ∴ A can do 1 work in 10 days
   Similarly,
   

   B can do 1 work in	5	× 9 = 15 days
   	3

   
   

   C can do 1 work in 8 ×	3	= 12 days.
   	2

   
   Now,
   

   A’s 1 day’s work =	1
   	10

   
   

   B’s 1 day’s work =	1
   	15

   
   

   C’s 1 day’s work =	1
   	12

   
   ∴ (A + B + C)’s 1 day’s work
   

   =	1	+	1	+	1
   	10		15		12

   
   

   =	6 + 4 + 5	=	15	=	1
   	60		60		4

   
   Hence, (A + B + C) together can complete the work in 4 days.

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