6. A can do a piece of work in 12 days and B in 24 days. If they work together, in how many days will they finish the work?

1. 1. 12 days

   
   
   

   2. 20 days

   
   
   

   3. 15 days

   
   
   

   4. 8 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   (A + B)’s 1 day’s work
   

   =	1	+	1
   	12		24

   
   

   =	2 + 1	=	3	=	1
   	24		24		8

   
   ∴ Required time = 8 days

   Correct Option: D

   (A + B)’s 1 day’s work
   

   =	1	+	1
   	12		24

   
   

   =	2 + 1	=	3	=	1
   	24		24		8

   
   ∴ Required time = 8 days

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7. A, B and C working separately can do a piece of work in 11 days, 20 days and 55 days respectively. In how many days, the work will be completed if A is assisted by B and C on alternate days ?

1. 1. 2

   
   
   

   2. 6

   
   
   

   3. 4

   
   
   

   4. 8

   
   
   

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1. View Hint View Answer Discuss in Forum

   (A + B)’s 1 day’s work
   

   =	1	+	1
   	11		20

   
   

   =	20 + 11	=	31
   	220		220

   
   (A + C)’s 1 day’s work
   

   =	1	+	1
   	11		55

   
   

   =	5 + 1	=	6
   	55		55

   
   Work done in first two days
   

   =	31	+	6
   	220		55

   
   

   =	31 + 24	=	55	=	1
   	220		220		4

   
   ∴ Required time = 2 × 4 = 8 days

   Correct Option: D

   (A + B)’s 1 day’s work
   

   =	1	+	1
   	11		20

   
   

   =	20 + 11	=	31
   	220		220

   
   (A + C)’s 1 day’s work
   

   =	1	+	1
   	11		55

   
   

   =	5 + 1	=	6
   	55		55

   
   Work done in first two days
   

   =	31	+	6
   	220		55

   
   

   =	31 + 24	=	55	=	1
   	220		220		4

   
   ∴ Required time = 2 × 4 = 8 days

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8. A and B together can do a piece of work in 9 days. If A does thrice the work of B in a given time, the time A alone will take to finish the work is

1. 1. 4 days

   
   
   

   2. 6 days

   
   
   

   3. 8 days

   
   
   

   4. 12 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let time taken by A be x days.
   ∴ Time taken by B = 3x days
   According to the question,
   

   ⇒	1	+	1	=	1
   	x		3x		9

   
   

   ⇒	3 + 1	=	1
   	3x		9

   
   ⇒ 3x = 4 × 9
   

   ⇒ x =	4 × 9	= 12 days
   	3

   Correct Option: D

   Let time taken by A be x days.
   ∴ Time taken by B = 3x days
   According to the question,
   

   ⇒	1	+	1	=	1
   	x		3x		9

   
   

   ⇒	3 + 1	=	1
   	3x		9

   
   ⇒ 3x = 4 × 9
   

   ⇒ x =	4 × 9	= 12 days
   	3

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9. X can do a piece of work in ‘p’ days and Y can do the same work in ‘q’ days. Then the number of days in which X and Y can together do that work is

1. 1. 	p + q
      	2

   
   
   

   2. 	1	+	1
      	p		q

   
   
   

   3. 	pq
      	p + q

   
   
   

   4. pq

   
   
   

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1. View Hint View Answer Discuss in Forum

   X’s 1 day’s work =	1
   	p

   
   

   Y’s 1 day’s work =	1
   	q

   
   (X + Y)’s 1 day’s work
   

   =	1	+	1	=	p + q
   	p		q		pq

   
   

   ∴ Required time =	pq
   	p + q

   Correct Option: C

   X’s 1 day’s work =	1
   	p

   
   

   Y’s 1 day’s work =	1
   	q

   
   (X + Y)’s 1 day’s work
   

   =	1	+	1	=	p + q
   	p		q		pq

   
   

   ∴ Required time =	pq
   	p + q

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10. If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days?

1. 1. 4 days

   
   
   

   2. 3 days

   
   
   

   3. 40 days

   
   
   

   4. 100 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   ∴	4 : 100		: : 100 : x
   	100 : 4

   
   ⇒ 4 × 100 × x = 100 × 100 × 4
   

   ⇒ x =	100 × 100 × 4	= 100 days
   	4 × 100

   Correct Option: D

   
   

   ∴	4 : 100		: : 100 : x
   	100 : 4

   
   ⇒ 4 × 100 × x = 100 × 100 × 4
   

   ⇒ x =	100 × 100 × 4	= 100 days
   	4 × 100

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