396. Janardan completes 2/3 of his work in 10 days. Time he will take to complete 3/5 of the same work, is

1. 1. 8 days

   
   
   

   2. 6 days

   
   
   

   3. 9 days

   
   
   

   4. 4 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   

   	M1D1	=	M2D2
   	W1		W2

   
   

   =	10	⇒	D2
   	2/5		3/5

   
   

   ⇒	30	=	5D2
   	2		3

   
   

   ⇒ D2 =	30	×	3	= 9 days
   	2		5

   Correct Option: C

   Using Rule 1,
   

   	M1D1	=	M2D2
   	W1		W2

   
   

   =	10	⇒	D2
   	2/5		3/5

   
   

   ⇒	30	=	5D2
   	2		3

   
   

   ⇒ D2 =	30	×	3	= 9 days
   	2		5

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397. A contractor was engaged to construct a road in 16 days. After working for 12 days with 20 labours it was found that only 5/8 th of the road had been constructed. To complete the work in stipulated time the number of extra labours required is :

1. 1. 18

   
   
   

   2. 10

   
   
   

   3. 12

   
   
   

   4. 16

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   Remaining work
   

   = 1 -	5	=	3	;
   	8		8

   
   Remaining time = 4 days
   

   	M1D1	=	M2D2
   	W1		W2

   
   

   =	20 × 12	=	M2 × 4
   	5/8		3/8

   
   

   =	20 × 12	=	M2 × 4
   	5		3

   
   

   ⇒ 4 × 12 =	M2 × 4
   	3

   
   ⇒ M₂ = 12 × 3 = 36
   ∴ Number of additional workers
   = 36 – 20 = 16

   Correct Option: D

   Using Rule 1,
   Remaining work
   

   = 1 -	5	=	3	;
   	8		8

   
   Remaining time = 4 days
   

   	M1D1	=	M2D2
   	W1		W2

   
   

   =	20 × 12	=	M2 × 4
   	5/8		3/8

   
   

   =	20 × 12	=	M2 × 4
   	5		3

   
   

   ⇒ 4 × 12 =	M2 × 4
   	3

   
   ⇒ M₂ = 12 × 3 = 36
   ∴ Number of additional workers
   = 36 – 20 = 16

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398. If 12 men working 8 hours a day complete the work in 10 days, how long would 16 men working
     

     7	1
     	2

     hours a day take to complete the same work?

1. 1. 7

   
   
   

   2. 6

   
   
   

   3. 10

   
   
   

   4. 8

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   
   

   ⇒ 16 ×	15	× x = 12 × 8 × 10
   	2

   
   ⇒ 8 × 15 × x = 12 × 8 × 10
   

   ⇒ x =	12 × 8 × 10	= 8 days
   	8 × 15

   Correct Option: D

   Using Rule 1,
   
   

   ⇒ 16 ×	15	× x = 12 × 8 × 10
   	2

   
   ⇒ 8 × 15 × x = 12 × 8 × 10
   

   ⇒ x =	12 × 8 × 10	= 8 days
   	8 × 15

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399. Jyothi can do	3	of a job in 12
     	4

     
     days. Mala is twice as efficient as Jyothi. In how many days will Mala finish the job ?

1. 1. 6 days

   
   
   

   2. 8 days

   
   
   

   3. 12 days

   
   
   

   4. 16 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   

   ∵ Jyothi can do	3	th of a job in 12 days
   	4

   
   ∴ Jyothi can do 1 job in
   

   	12 × 4	= 16 days
   	3

   
   As Mala is twice as efficient as Jyothi,
   ∴ Mala will finish the job in 8 days

   Correct Option: B

   Using Rule 1,
   

   ∵ Jyothi can do	3	th of a job in 12 days
   	4

   
   ∴ Jyothi can do 1 job in
   

   	12 × 4	= 16 days
   	3

   
   As Mala is twice as efficient as Jyothi,
   ∴ Mala will finish the job in 8 days

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400. 4 men and 6 women complete a work in 8 days. 2 men and 9 women also complete in 8 days in which. The number of days in which 18 women complete the work is :

1. 1. 4	1	days
      	3

   
   
   

   2. 5	1	days
      	3

   
   
   

   3. 4	2	days
      	3

   
   
   

   4. 5	2	days
      	3

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to the question,
   (4 × 8) men + (6 × 8) women ≡ (2 × 8) men + (9 × 8) women
   ⇒ 4 men + 6 women ≡ 2 men + 9 women
   ⇒ (4 – 2) men ≡ (9 – 6) women
   ⇒ 2 men ≡ 3 women
   ∴ 4 men + 6 women ≡ 12 women
   ∴ M₁D₁ = M₂D₂
   ⇒ 12 × 8 = 18 × D₂
   

   ⇒ D2 =	12 × 8
   	18

   
   

   =	16	= 5	1	days
   	3		3

   
   Aliter : Using Rule 1,
   Here, A₁ = 4, B₁ = 6, D₁ = 8
   A₂ = 2, B₂ = 9, D₂ = 8
   A₃ = 0, B₃ = 18
   Required time
   

   =	D1D2(A1B2 - A2B1)
   	D1(A1B3 - A3B1) - D2(A2B3 - A3B2)

   
   

   =	8 × 8(4 × 9 - 2 × 6)
   	8(4 × 18 - 0 × 6) - 8(2 × 18 - 0 × 6)

   
   

   =	64 × 24	=	192
   	8 × 72 - 36 × 8		36

   
   

   =	16	= 5	1	days
   	3		3

   Correct Option: B

   According to the question,
   (4 × 8) men + (6 × 8) women ≡ (2 × 8) men + (9 × 8) women
   ⇒ 4 men + 6 women ≡ 2 men + 9 women
   ⇒ (4 – 2) men ≡ (9 – 6) women
   ⇒ 2 men ≡ 3 women
   ∴ 4 men + 6 women ≡ 12 women
   ∴ M₁D₁ = M₂D₂
   ⇒ 12 × 8 = 18 × D₂
   

   ⇒ D2 =	12 × 8
   	18

   
   

   =	16	= 5	1	days
   	3		3

   
   Aliter : Using Rule 1,
   Here, A₁ = 4, B₁ = 6, D₁ = 8
   A₂ = 2, B₂ = 9, D₂ = 8
   A₃ = 0, B₃ = 18
   Required time
   

   =	D1D2(A1B2 - A2B1)
   	D1(A1B3 - A3B1) - D2(A2B3 - A3B2)

   
   

   =	8 × 8(4 × 9 - 2 × 6)
   	8(4 × 18 - 0 × 6) - 8(2 × 18 - 0 × 6)

   
   

   =	64 × 24	=	192
   	8 × 72 - 36 × 8		36

   
   

   =	16	= 5	1	days
   	3		3

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