191. If 10 men can do a piece of work in 12 days, the time taken by 12 men to do the same piece of work will be

1. 1. 12 days

   
   
   

   2. 10 days

   
   
   

   3. 9 days

   
   
   

   4. 8 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   Where = number of days
   ⇒ 12 : 10 :: 12 : x
   ⇒ 12 × x = 10 × 12
   

   ⇒x =	10 × 12	= 10 days
   	12

   
   Aliter : Using Rule 1,
   Here, M₁ = 10, D₁ = 12
   M₂ = 12, D₂ = ?
   M₁D₁ = M₂D₂
   10 × 12 = 12 × D₂
   D₂ = 10 days

   Correct Option: B

   
   Where = number of days
   ⇒ 12 : 10 :: 12 : x
   ⇒ 12 × x = 10 × 12
   

   ⇒x =	10 × 12	= 10 days
   	12

   
   Aliter : Using Rule 1,
   Here, M₁ = 10, D₁ = 12
   M₂ = 12, D₂ = ?
   M₁D₁ = M₂D₂
   10 × 12 = 12 × D₂
   D₂ = 10 days

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192. 7 men can complete a piece of work in 12 days. How many additional men will be required to complete double the work in 8 days ?

1. 1. 28

   
   
   

   2. 21

   
   
   

   3. 14

   
   
   

   4. 7

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   ∴	1 : 2		: : 7 : x
   	8 : 12

   
   where, x is no. of men
   ⇒ 1 × 8 × x = 2 × 12 × 7
   

   ⇒ x =	2 × 12 × 7	= 21
   	8

   
   ∴ Number of additional men
   = 21 – 7 = 14
   Metod 2 :
   Using Rule 1,
   M₁D₁W₂ = M₂D₂W₁
   ⇒ 7 × 12 × 2 = M₂ × 8 × 1
   

   ⇒ M2 =	7 × 12 × 2	= 21
   	8

   
   ∴ No. of additional men
   = 21 – 7 = 14

   Correct Option: C

   
   

   ∴	1 : 2		: : 7 : x
   	8 : 12

   
   where, x is no. of men
   ⇒ 1 × 8 × x = 2 × 12 × 7
   

   ⇒ x =	2 × 12 × 7	= 21
   	8

   
   ∴ Number of additional men
   = 21 – 7 = 14
   Metod 2 :
   Using Rule 1,
   M₁D₁W₂ = M₂D₂W₁
   ⇒ 7 × 12 × 2 = M₂ × 8 × 1
   

   ⇒ M2 =	7 × 12 × 2	= 21
   	8

   
   ∴ No. of additional men
   = 21 – 7 = 14

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193. ‘x’ number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. The original number of men is

1. 1. 6

   
   
   

   2. 10

   
   
   

   3. 12

   
   
   

   4. 15

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   x + 6 : x : : 30 : 20
   

   ⇒	x + 6	=	30	=	3
   	x		20		2

   
   ⇒ 2x + 12 = 3x
   ⇒ 3x – 2x = 12
   ⇒ x = 12
   Aliter : Using Rule 1,
   Here, M₁ = x, D₁ = 30
   M₂ = x + 6, D₂ = 20
   M₁D₁ = M₂D₂
   x × 30 = (x + 6) × 20
   3x = 2 x + 12
   x = 12

   Correct Option: C

   
   x + 6 : x : : 30 : 20
   

   ⇒	x + 6	=	30	=	3
   	x		20		2

   
   ⇒ 2x + 12 = 3x
   ⇒ 3x – 2x = 12
   ⇒ x = 12
   Aliter : Using Rule 1,
   Here, M₁ = x, D₁ = 30
   M₂ = x + 6, D₂ = 20
   M₁D₁ = M₂D₂
   x × 30 = (x + 6) × 20
   3x = 2 x + 12
   x = 12

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194. Some carpenters promised to do a job in 9 days but 5 of them were absent and remaining men did the job in 12 days. The original number of carpenters was

1. 1. 24

   
   
   

   2. 20

   
   
   

   3. 16

   
   
   

   4. 18

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   Let the original number of carpenters be x.
   M₁D₁ = M₂D₂
   ⇒ x × 9 = (x – 5) × 12
   ⇒ 9x = 12x – 60
   ⇒ 3x = 60 ⇒ x = 20

   Correct Option: B

   Using Rule 1,
   Let the original number of carpenters be x.
   M₁D₁ = M₂D₂
   ⇒ x × 9 = (x – 5) × 12
   ⇒ 9x = 12x – 60
   ⇒ 3x = 60 ⇒ x = 20

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195. 2 men and 3 women together or 4 men together can complete a piece of work in 20 days.3 men and 3 women will complete the same work in :

1. 1. 12 days

   
   
   

   2. 16 days

   
   
   

   3. 18 days

   
   
   

   4. 19 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   2 men + 3 women ≡ 4 men
   ⇒ 2 men ≡ 3 women
   ∴ 3 men + 3 women ≡ 5 men
   ∴ M₁D₁ = M₂D₂
   ⇒ 4 × 20 = 5 × D₂
   

   ⇒ D2 =	4 × 20	= 16 days
   	5

   Correct Option: B

   Using Rule 1,
   2 men + 3 women ≡ 4 men
   ⇒ 2 men ≡ 3 women
   ∴ 3 men + 3 women ≡ 5 men
   ∴ M₁D₁ = M₂D₂
   ⇒ 4 × 20 = 5 × D₂
   

   ⇒ D2 =	4 × 20	= 16 days
   	5

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