421. A can do a certain job in 12 days. B is 60% more efficient than A. To do the same job B alone would take :

1. 1. 7	1	days
      	2

   
   
   

   2. 8 days

   
   
   

   3. 10 days

   
   
   

   4. 7 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Time taken by B
   

   = 12 ×	100	=	15	= 7	1
   	160		2		2

   
   Aliter : Using Rule 17,
   Here, x = 12, R = 60%
   Time taken by B
   

   = x ×	100	days
   	100 + R

   
   

   = 12 ×	100	days
   	160

   
   

   =	15	= 7	1	days
   	2		2

   Correct Option: A

   Time taken by B
   

   = 12 ×	100	=	15	= 7	1
   	160		2		2

   
   Aliter : Using Rule 17,
   Here, x = 12, R = 60%
   Time taken by B
   

   = x ×	100	days
   	100 + R

   
   

   = 12 ×	100	days
   	160

   
   

   =	15	= 7	1	days
   	2		2

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422. 5 men and 2 women working together can do four times as much work per hour as a man and a woman together. The work done by a man and a woman should be in the ratio :

1. 1. 1 : 2

   
   
   

   2. 2 : 1

   
   
   

   3. 1 : 3

   
   
   

   4. 4 : 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   5m + 2w = 4m + 4w
   ⇒ m = 2w
   ∴ Required ratio = 2 : 1

   Correct Option: B

   5m + 2w = 4m + 4w
   ⇒ m = 2w
   ∴ Required ratio = 2 : 1

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423. A is 30% more efficient than B, and can alone do a work in 23 days. The number of days, in which A and B, working together can finish the job is

1. 1. 11 days

   
   
   

   2. 13 days

   
   
   

   3. 20 days

   
   
   

   4. 21 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 2,
   Time taken by B
   

   =	130	× 23 =	299	days
   	100		10

   
   (A + B)’s 1 day’s work
   

   =	1	+	10
   	23		299

   
   

   =	13 + 10	=	23	=	1
   	299		299		13

   
   ∴ Time taken by (A + B) = 13 days

   Correct Option: B

   Using Rule 2,
   Time taken by B
   

   =	130	× 23 =	299	days
   	100		10

   
   (A + B)’s 1 day’s work
   

   =	1	+	10
   	23		299

   
   

   =	13 + 10	=	23	=	1
   	299		299		13

   
   ∴ Time taken by (A + B) = 13 days

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424. A can do a work in 9 days, if B is 50% more efficient than A, then in how many days can B do the same work?

1. 1. 13.5 days

   
   
   

   2. 4.5 days

   
   
   

   3. 6 days

   
   
   

   4. 3 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Time taken by
   

   B = 9 ×	100	= 6 days
   	150

   
   Aliter : Using Rule 17,
   Here, x = 9, R = 50%
   Time taken by B
   

   = x ×	100	days
   	100 + R

   
   

   = 9 ×	100	= 6 days
   	150

   Correct Option: C

   Time taken by
   

   B = 9 ×	100	= 6 days
   	150

   
   Aliter : Using Rule 17,
   Here, x = 9, R = 50%
   Time taken by B
   

   = x ×	100	days
   	100 + R

   
   

   = 9 ×	100	= 6 days
   	150

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425. A takes 10 days less than the time taken by B to finish a piece of work. If both A and B can do it in 12 days, then the time taken by B alone to finish the work is

1. 1. 30 days

   
   
   

   2. 27 days

   
   
   

   3. 20 days

   
   
   

   4. 25 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 2,
   Let time taken by B in completing the work = x days
   ∴ Time taken by A = (x – 10) days
   

   ∴	1	+	1	=	1
   	x		x - 10		12

   
   

   ⇒	x - 10 + x	=	1
   	x(x - 10)		12

   
   ⇒ 24x – 120 = x² – 10x
   ⇒ x² – 34x + 120 = 0
   ⇒ x² – 30x – 4x + 120 = 0
   ⇒ x (x – 30) – 4 (x – 30) = 0
   ⇒ (x – 4) (x – 30) = 0
   ⇒ x = 30 because x ≠ 4

   Correct Option: A

   Using Rule 2,
   Let time taken by B in completing the work = x days
   ∴ Time taken by A = (x – 10) days
   

   ∴	1	+	1	=	1
   	x		x - 10		12

   
   

   ⇒	x - 10 + x	=	1
   	x(x - 10)		12

   
   ⇒ 24x – 120 = x² – 10x
   ⇒ x² – 34x + 120 = 0
   ⇒ x² – 30x – 4x + 120 = 0
   ⇒ x (x – 30) – 4 (x – 30) = 0
   ⇒ (x – 4) (x – 30) = 0
   ⇒ x = 30 because x ≠ 4

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