271. A work can be completed by P and Q in 12 days, Q and R in 15 days, R and P in 20 days. In how many days P alone can finish the work?

1. 1. 10 days

   
   
   

   2. 20 days

   
   
   

   3. 30 days

   
   
   

   4. 60 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   (P + Q)’s 1 day’s work =	1	.......(i)
   	12

   
   

   (Q + R)’s 1 day’s work =	1	.......(ii)
   	15

   
   

   (R + P)’s 1 day’s work =	1	.......(iii)
   	20

   
   Adding all three equations,
   

   2 (P + Q + R)’s 1 day’s work =	1	+	1	+	1
   	12		15		20

   
   

   Correct Option: C

   (P + Q)’s 1 day’s work =	1	.......(i)
   	12

   
   

   (Q + R)’s 1 day’s work =	1	.......(ii)
   	15

   
   

   (R + P)’s 1 day’s work =	1	.......(iii)
   	20

   
   Adding all three equations,
   

   2 (P + Q + R)’s 1 day’s work =	1	+	1	+	1
   	12		15		20

   
   

   2 (P + Q + R)’s 1 day’s work =	5 + 4 + 3	=	1
   	60		5

   
   

   ∴ (P + Q + R)’s 1 day’s work =	1	.......(iv)
   	10

   
   

   ∴ P’s 1 day’s work =	1	-	1
   	10		15

   
   

   P’s 1 day’s work =	3 - 2	=	1
   	30		30

   
   ∴ P alone will complete the work in 30 days.

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272. A and B can complete a piece of work in 8 days, B and C can do it in 12 days, C and A can do it in 8 days. A, B and C together can complete it in

1. 1. 4 days

   
   
   

   2. 5 days

   
   
   

   3. 6 days

   
   
   

   4. 7 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   (A + B)’s 1 day’s work =	1
   	8

   
   

   (B + C)’s 1 day’s work =	1
   	12

   
   

   (C + A)’s 1 day’s work =	1
   	8

   
   On adding ,
   

   2 (A + B + C)’s 1 day’s work =	1	+	1	+	1
   	8		12		8

   
   

   2 (A + B + C)’s 1 day’s work =	3 + 2 + 3
   	24

   
   

   2 (A + B + C)’s 1 day’s work =	8	=	1
   	24		3

   
   

   ∴ (A + B + C)’s 1 day’s work =	1
   	6

   
   Hence, the work will be completed in 6 days.
   2nd Method to solve this question :
   

   Correct Option: C

   (A + B)’s 1 day’s work =	1
   	8

   
   

   (B + C)’s 1 day’s work =	1
   	12

   
   

   (C + A)’s 1 day’s work =	1
   	8

   
   On adding ,
   

   2 (A + B + C)’s 1 day’s work =	1	+	1	+	1
   	8		12		8

   
   

   2 (A + B + C)’s 1 day’s work =	3 + 2 + 3
   	24

   
   

   2 (A + B + C)’s 1 day’s work =	8	=	1
   	24		3

   
   

   ∴ (A + B + C)’s 1 day’s work =	1
   	6

   
   Hence, the work will be completed in 6 days.
   2nd Method to solve this question :
   

   Time =	2xyz
   	xy + yz + zx

   
   Here, x = 8, y = 12; z = 8
   

   Time =	2 × 8 × 12 × 8	=	2 × 8 × 12 × 8	= 6 days
   	96 + 96 + 64		256

   
   

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273. 'A' can do a piece of work in x days and B can do the same work 3x days. To finish the work together they take 12 days. What is the value of x ?

1. 1. 8

   
   
   

   2. 10

   
   
   

   3. 12

   
   
   

   4. 16

   
   
   

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1. View Hint View Answer Discuss in Forum

   A's 1 day's work A = 1/x
   B's 1 day's work B = 1/3x
   (A + B)'s 1 day's work = (1/x) + (1/3x) = 4/3x
   And given one day work of both A and B = 1/12
   ⇒ 4/3x = 1/12

   Correct Option: D

   A's 1 day's work A = 1/x
   B's 1 day's work B = 1/3x
   (A + B)'s 1 day's work = (1/x) + (1/3x) = 4/3x
   And given one day work of both A and B = 1/12
   ⇒ 4/3x = 1/12
   ⇒ 3x = 48
   ⇒ x =16

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274. A and B working together; can do a piece of work in 4	1	hours. B and C working together
     	2

     
     

     can do it in 3 hours. C and A working together can do it in 2	1	hours. All of them
     	4

     begin the work at the same time. Find how much time they will take to finish the piece of work.

1. 1. 3 hours

   
   
   

   2. 2 hours

   
   
   

   3. 2·5 hours

   
   
   

   4. 3·25 hours

   
   
   

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1. View Hint View Answer Discuss in Forum

   (A + B)’s 1 hour’s work =	2	.......(i)
   	9

   
   

   (B + C)’s 1 hour’s work =	1	.......(ii)
   	3

   
   

   (C + A)’s 1 hour’s work =	4	.......(iii)
   	9

   
   Adding all three equations,
   

   2 (A + B + C)’s 1 hour’s work =	2	+	1	+	4
   	9		3		9

   
   

   2 (A + B + C)’s 1 hour’s work =	2 + 3 + 4	= 1
   	9

   
   ∴ A, B and C together will complete the work in 2 hours.
   Second method to solve this question ,
   Here , x = 9 / 2 , y = 3 , z = 9 / 4
   

   Correct Option: B

   (A + B)’s 1 hour’s work =	2	.......(i)
   	9

   
   

   (B + C)’s 1 hour’s work =	1	.......(ii)
   	3

   
   

   (C + A)’s 1 hour’s work =	4	.......(iii)
   	9

   
   Adding all three equations,
   

   2 (A + B + C)’s 1 hour’s work =	2	+	1	+	4
   	9		3		9

   
   

   2 (A + B + C)’s 1 hour’s work =	2 + 3 + 4	= 1
   	9

   
   ∴ A, B and C together will complete the work in 2 hours.
   Second method to solve this question ,
   Here , x = 9 / 2 , y = 3 , z = 9 / 4
   

   Time taken =			2 ×	9	× 3 ×	9
   				2		4
   	9	× 3 + 3 ×	9	+	9	×	9
   	2		4		2		4

   
   

   Time taken =	( 18 × 27 ) / 8
   	{ ( 27/2 ) + ( 27/4 ) + ( 81/8 ) }

   
   

   Time taken =	18 × 27	×	8
   	8		( 108 + 54 + 81 )

   
   

   Time taken =	18 × 27	= 2 hours
   	243

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275. A and B together can complete a piece of work in 18 days, B and C in 24 days and A and C in 36 days. In how many days, will all of them together complete the work ?

1. 1. 16 days

   
   
   

   2. 15 days

   
   
   

   3. 12 days

   
   
   

   4. 10 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   (A + B)’s 1 day’s work =	1
   	18

   
   

   (B + C)’s 1 day’s work =	1
   	24

   
   

   (A + C)’s 1 day’s work =	1
   	36

   
   Adding all three,
   

   2 (A + B + C)’s 1 day’s work =	1	+	1	+	1
   	18		24		36

   
   

   2 (A + B + C)’s 1 day’s work =	4 + 3 + 2	=	1
   	72		8

   
   

   ∴ (A + B + C)’ 1 day’s work =	1
   	16

   
   ∴ A, B and C together will complete the work in 16 days.
   Second method to solve this question ,
   Here , x = 18 , y = 24 , z = 36
   

   Time taken =	2xyz
   	xy + yz + zx

   
   

   Correct Option: A

   (A + B)’s 1 day’s work =	1
   	18

   
   

   (B + C)’s 1 day’s work =	1
   	24

   
   

   (A + C)’s 1 day’s work =	1
   	36

   
   Adding all three,
   

   2 (A + B + C)’s 1 day’s work =	1	+	1	+	1
   	18		24		36

   
   

   2 (A + B + C)’s 1 day’s work =	4 + 3 + 2	=	1
   	72		8

   
   

   ∴ (A + B + C)’ 1 day’s work =	1
   	16

   
   ∴ A, B and C together will complete the work in 16 days.
   Second method to solve this question ,
   Here , x = 18 , y = 24 , z = 36
   

   Time taken =	2xyz
   	xy + yz + zx

   
   

   Total time taken =	2 × 18 × 24 × 36
   	18 × 24 + 24 × 36 + 36 × 18

   
   

   Total time taken =	36 × 24 × 36
   	432 + 864 + 648

   
   

   Total time taken =	31104	= 16 days
   	1944

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