166. Working 8 hours a day, Anu can copy a book in 18 days. How many hours a day should she work so as to finish the work in 12 days ?

1. 1. 12 hours

   
   
   

   2. 10 hours

   
   
   

   3. 11 hours

   
   
   

   4. 13 hours

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   ⇒	12	=	8
   	18		x

   
   where x is hours/days
   ⇒ 12x = 18 × 8
   

   ⇒ x =	18 × 8	= 12 hours
   	12

   
   Aliter : Using Rule 1,
   Here, M₁ = 1, D₁= 18, T₁ = 8
   M₂ = 1, D₂ = 12, T₂ = ?
   M₁D₁T₁ = M₂D₂T₂
   1 × 18 × 8 = 1 × 12 × T₂
   

   T2 =	18 × 8	= 12 hours
   	12

   Correct Option: A

   
   

   ⇒	12	=	8
   	18		x

   
   where x is hours/days
   ⇒ 12x = 18 × 8
   

   ⇒ x =	18 × 8	= 12 hours
   	12

   
   Aliter : Using Rule 1,
   Here, M₁ = 1, D₁= 18, T₁ = 8
   M₂ = 1, D₂ = 12, T₂ = ?
   M₁D₁T₁ = M₂D₂T₂
   1 × 18 × 8 = 1 × 12 × T₂
   

   T2 =	18 × 8	= 12 hours
   	12

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167. A contractor undertook to finish a work in 92 days and employed 110 men. After 48 days, he found that he had already done 3/5 part of the work, the number of men he can withdraw so that the work may still be finished in time is :

1. 1. 45

   
   
   

   2. 40

   
   
   

   3. 35

   
   
   

   4. 30

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   

   	M1D1	=	M2D2
   	W1		W2

   
   

   ⇒	110 × 48	=	M2 × 44
   	3		2
   	5		5

   
   ⇒ M₂ × 44 × 3 = 110 × 48 × 2
   

   ⇒ M2 =	110 × 48 × 2	= 80
   	44 × 3

   
   ∴ Number of men can be withdrawn
   = 110 – 80 = 30

   Correct Option: D

   Using Rule 1,
   

   	M1D1	=	M2D2
   	W1		W2

   
   

   ⇒	110 × 48	=	M2 × 44
   	3		2
   	5		5

   
   ⇒ M₂ × 44 × 3 = 110 × 48 × 2
   

   ⇒ M2 =	110 × 48 × 2	= 80
   	44 × 3

   
   ∴ Number of men can be withdrawn
   = 110 – 80 = 30

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168. A man undertakes to do a certain work in 150 days. He employs 200 men. He finds that only a quarter of the work is done in 50 days. The number of additional men that should be appointed so that the whole work will be finished in time is :

1. 1. 75

   
   
   

   2. 100

   
   
   

   3. 125

   
   
   

   4. 50

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   

   200 men do	1	work in 50 days.
   	4

   
   

   ∴	M1D1	=	M2D2
   	W1		W2

   
   

   ⇒	200 × 50	=	M2 × 100
   	1		3
   	4		4

   
   ⇒ M₂ × 100 = 200 × 50 × 3
   ⇒ M₂ = 300
   ∴ Additional men = 100

   Correct Option: B

   Using Rule 1,
   

   200 men do	1	work in 50 days.
   	4

   
   

   ∴	M1D1	=	M2D2
   	W1		W2

   
   

   ⇒	200 × 50	=	M2 × 100
   	1		3
   	4		4

   
   ⇒ M₂ × 100 = 200 × 50 × 3
   ⇒ M₂ = 300
   ∴ Additional men = 100

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169. A contractor undertook to finish a certain work in 124 days and employed 120 men. After 64 days, he found that he had already done 2/3 of the work.
     How many men can be discharged now so that the work may finish in time ?

1. 1. 48

   
   
   

   2. 56

   
   
   

   3. 40

   
   
   

   4. 50

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   

   Remaining work = 1 -	2	=	1
   	3		3

   
   Remaining days = 124–64= 60
   

   ∴	M1D1	=	M2D2
   	W1		W2

   
   

   ⇒	120 × 64	=	M2 × 60
   	2		1
   	3		3

   
   

   ⇒ M2 =	120 × 64	= 64
   	2 × 60

   
   ∴ No. of men can be discharged
   = 120 – 64 = 56 men

   Correct Option: B

   Using Rule 1,
   

   Remaining work = 1 -	2	=	1
   	3		3

   
   Remaining days = 124–64= 60
   

   ∴	M1D1	=	M2D2
   	W1		W2

   
   

   ⇒	120 × 64	=	M2 × 60
   	2		1
   	3		3

   
   

   ⇒ M2 =	120 × 64	= 64
   	2 × 60

   
   ∴ No. of men can be discharged
   = 120 – 64 = 56 men

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170. If 7 men working 7 hrs a day for each of 7 days produce 7 units of work, then the units of work produced by 5 men working 5 hrs a day for each of 5 days is

1. 1. 25

      343

   
   
   

   2. 125

      49

   
   
   

   3. 49

      125

   
   
   

   4. 343

      25

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   

   ∴	M1D1T1	=	M2D2T2
   	W1		W2

   
   

   ⇒	7 × 7 × 7	=	5 × 5 × 5
   	7		W2

   
   ⇒ 49 × W₂ = 125
   

   ⇒ W2 =	125
   	49

   Correct Option: B

   Using Rule 1,
   

   ∴	M1D1T1	=	M2D2T2
   	W1		W2

   
   

   ⇒	7 × 7 × 7	=	5 × 5 × 5
   	7		W2

   
   ⇒ 49 × W₂ = 125
   

   ⇒ W2 =	125
   	49

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