11. 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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12. A can do a piece of work in 12 days and B in 20 days. If they together work on it for 5 days, and remaining work is completed by C in 3 days, then in how many days can C do the same work alone?

1. 1. 10 days

   
   
   

   2. 9 days

   
   
   

   3. 12 days

   
   
   

   4. 15 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Work done by (A + B) in 5 days
   

   = 5		1	+	1		= 5		5 + 3
   		15		20				60

   
   

   =	40	=	2
   	60		3

   
   

   Remaining work = 1 -	2	=	1
   	3		3

   
   

   ∵ Time taken by C in doing	1	work = 3 days
   	3

   
   ∴ Required time = 3 × 3 = 9 days

   Correct Option: B

   Work done by (A + B) in 5 days
   

   = 5		1	+	1		= 5		5 + 3
   		15		20				60

   
   

   =	40	=	2
   	60		3

   
   

   Remaining work = 1 -	2	=	1
   	3		3

   
   

   ∵ Time taken by C in doing	1	work = 3 days
   	3

   
   ∴ Required time = 3 × 3 = 9 days

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13. A man can do a piece of work in 30 hours. If he works with his son then the same piece of work is finished in 20 hours. If the son works alone he can do the work in

1. 1. 60 hours

   
   
   

   2. 50 hours

   
   
   

   3. 25 hours

   
   
   

   4. 10 hours

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let time taken by son be x hours.
   ∴ Father’s and son’s 1 day’s work
   

   =	1	+	1
   	30		x

   
   

   ∴	1	+	1	=	1
   	30		x		20

   
   

   ⇒	1	=	1	-	1
   	x		20		30

   
   

   =	3 - 2	=	1
   	60		60

   
   ∴ x = 60 hours

   Correct Option: A

   Let time taken by son be x hours.
   ∴ Father’s and son’s 1 day’s work
   

   =	1	+	1
   	30		x

   
   

   ∴	1	+	1	=	1
   	30		x		20

   
   

   ⇒	1	=	1	-	1
   	x		20		30

   
   

   =	3 - 2	=	1
   	60		60

   
   ∴ x = 60 hours

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14. 16 men are able to complete a piece of work in 12 days working 14 hours a day. How long will 28 men, working 12 hours a day, take to complete the work ?

1. 1. 10 days

   
   
   

   2. 7 days

   
   
   

   3. 8 days

   
   
   

   4. 6 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   
   

   ∴	28 : 16		: : 12 : x
   	12 : 14

   
   ⇒ 28 × 12 × x =16 × 14 × 12
   

   ⇒ x =	16 × 14 × 12	= 8 days
   	28 × 12

   Correct Option: C

   Using Rule 1,
   
   

   ∴	28 : 16		: : 12 : x
   	12 : 14

   
   ⇒ 28 × 12 × x =16 × 14 × 12
   

   ⇒ x =	16 × 14 × 12	= 8 days
   	28 × 12

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15. A’s 2 days’ work is equal to B’s 3 days’ work. If A can complete the work in 8 days then to complete the work B will take

1. 1. 14 days

   
   
   

   2. 12 days

   
   
   

   3. 15 days

   
   
   

   4. 16 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   A’s 2 days’ work = B’s 3 days’ work
   ∴ Time taken by A = 8 days
   

   ∴ Time taken by B =	8	× 3 = 12 days
   	2

   Correct Option: B

   A’s 2 days’ work = B’s 3 days’ work
   ∴ Time taken by A = 8 days
   

   ∴ Time taken by B =	8	× 3 = 12 days
   	2

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