186. A and B undertook to do a piece of work for ₹ 4500. A alone could do it in 8 days and B alone in 12 days. With the assistance of C they finished the work in 4 days. Then C’s share of the money is

1. 1. ₹ 2250

   
   
   

   2. ₹ 1500

   
   
   

   3. ₹ 750

   
   
   

   4. ₹ 375

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 25,
   C’s 1 day’s work
   

   =	1	-		1	+	1
   	4			8		12

   
   

   =	1	-		3 + 2
   	4			24

   
   

   =	1	-	1	=	6 - 5	=	1
   	4		24		24		24

   
   

   A : B : C =	1	:	1	:	1	= 3 : 2 : 1
   	8		12		24

   
   

   C’s share = ₹		1	× 4500		= ₹ 750
   		6

   Correct Option: C

   Using Rule 25,
   C’s 1 day’s work
   

   =	1	-		1	+	1
   	4			8		12

   
   

   =	1	-		3 + 2
   	4			24

   
   

   =	1	-	1	=	6 - 5	=	1
   	4		24		24		24

   
   

   A : B : C =	1	:	1	:	1	= 3 : 2 : 1
   	8		12		24

   
   

   C’s share = ₹		1	× 4500		= ₹ 750
   		6

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187. 4 mat-weavers can weave 4 mats in 4 days. At the same rate how many mats would be woven by 8 mat-weavers in 8 days ?

1. 1. 4

   
   
   

   2. 8

   
   
   

   3. 12

   
   
   

   4. 16

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   
   

   	4 : 8		: : 4 : x
   	4 : 8

   
   where, x is no. of mats
   ⇒ 4 × 4 × x = 8 × 8 × 4
   

   ∴ x =	8 × 8 × 4	= 16
   	4 × 4

   Correct Option: D

   Using Rule 1,
   
   

   	4 : 8		: : 4 : x
   	4 : 8

   
   where, x is no. of mats
   ⇒ 4 × 4 × x = 8 × 8 × 4
   

   ∴ x =	8 × 8 × 4	= 16
   	4 × 4

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188. 10 men working 6 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the same work in 12 days ?

1. 1. 6 days

   
   
   

   2. 10 days

   
   
   

   3. 12 days

   
   
   

   4. 15 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   
   where, x is working hrs/days
   

   ∴	15 : 10		: : 6 : x
   	12 : 18

   
   ⇒ 15 × 12 × x = 10 × 18 × 6
   

   ∴ x =	10 × 18 × 6	= 6 hours
   	15 × 12

   Correct Option: A

   Using Rule 1,
   
   where, x is working hrs/days
   

   ∴	15 : 10		: : 6 : x
   	12 : 18

   
   ⇒ 15 × 12 × x = 10 × 18 × 6
   

   ∴ x =	10 × 18 × 6	= 6 hours
   	15 × 12

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189. Two persons can complete a piece of work in 9 days. How many more persons are needed to complete double the work in 12 days?

1. 1. 3

   
   
   

   2. 2

   
   
   

   3. 4

   
   
   

   4. 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   where x = number of persons
   

   	1 : 2		: : 2 : x
   	12 : 9

   
   ⇒ 1× 12 × x = 2 × 9 × 2
   

   ⇒ x =	2 × 9 × 2	= 3
   	12

   
   Aliter : Using Rule 1,
   Here, M₁ = 2, W₁ = 1, D₁ = 9
   M₂ = ?, W₂ = 2, D₂ = 12
   M₁D₁W₂ = M₂D₂W₁
   2 × 9 × 2 = M₂ × 12 × 1
   

   ⇒ M2 =	36	M2 = 3
   	12

   Correct Option: A

   
   where x = number of persons
   

   	1 : 2		: : 2 : x
   	12 : 9

   
   ⇒ 1× 12 × x = 2 × 9 × 2
   

   ⇒ x =	2 × 9 × 2	= 3
   	12

   
   Aliter : Using Rule 1,
   Here, M₁ = 2, W₁ = 1, D₁ = 9
   M₂ = ?, W₂ = 2, D₂ = 12
   M₁D₁W₂ = M₂D₂W₁
   2 × 9 × 2 = M₂ × 12 × 1
   

   ⇒ M2 =	36	M2 = 3
   	12

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190. If p men working p hours per day for p days produce p units of work, then the units of work produced by n men working n hours a day for n days is

1. 1. p2

      n2

   
   
   

   2. p3

      n2

   
   
   

   3. n2

      p2

   
   
   

   4. n3

      p2

   
   
   

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1. View Hint View Answer Discuss in Forum

   ∵ P men working P hours/day for P days produce P units of work.
   ∴ 1 man working 1 hour/day for 1 day produce
   

   	p	=	1	units of work
   	p3		p2

   
   ∴ n men working n hours a da for n day’s produce
   

   	n3	units of work
   	p2

   
   Aliter : Using Rule 1,
   Here, M₁ = p, D₁ = p, T₁ =p,W₁ = p
   M₂ = n, D₂ = n, T₂ = n, W₂ = ?
   M₁D₁T₁W₂ = M₂D₂T₂W₁
   p × p × p × w₂ = n × n × n × p
   

   w2 =	n3
   	p2

   Correct Option: D

   ∵ P men working P hours/day for P days produce P units of work.
   ∴ 1 man working 1 hour/day for 1 day produce
   

   	p	=	1	units of work
   	p3		p2

   
   ∴ n men working n hours a da for n day’s produce
   

   	n3	units of work
   	p2

   
   Aliter : Using Rule 1,
   Here, M₁ = p, D₁ = p, T₁ =p,W₁ = p
   M₂ = n, D₂ = n, T₂ = n, W₂ = ?
   M₁D₁T₁W₂ = M₂D₂T₂W₁
   p × p × p × w₂ = n × n × n × p
   

   w2 =	n3
   	p2

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