46. A father can do a job as fast as his two sons working together. If one son does the job in 3 hours and the other in 6 hours, the number of hours taken by the father, to do the job alone is

1. 1. 1

   
   
   

   2. 2

   
   
   

   3. 3

   
   
   

   4. 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   Work done by two sons in an hour
   

   =	1	+	1	=	1
   	3		6		2

   
   ∴ Work done by father in an hour
   

   =	1
   	2

   
   ∴ Required time = 2 hours

   Correct Option: B

   Work done by two sons in an hour
   

   =	1	+	1	=	1
   	3		6		2

   
   ∴ Work done by father in an hour
   

   =	1
   	2

   
   ∴ Required time = 2 hours

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47. If 42 persons consume 144 kg of wheat in 15 days, then in how many days will 30 persons consume 45 kg of wheat ?

1. 1. 8 days

   
   
   

   2. 7 days

   
   
   

   3. 12 days

   
   
   

   4. 6 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   ∴	30 : 42		: : 15 : x
   	144 : 48

   
   ⇒ 30 × 144 × x = 42 × 48 × 15
   

   ⇒ x =	42 × 48 × 15	= 7 days
   	30 × 144

   Correct Option: B

   
   

   ∴	30 : 42		: : 15 : x
   	144 : 48

   
   ⇒ 30 × 144 × x = 42 × 48 × 15
   

   ⇒ x =	42 × 48 × 15	= 7 days
   	30 × 144

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48. A can do as much work in 4 days as B can do in 5 days, and B can do as much work in 6 days as C in 7 days. In what time will C do a piece of work which A can do in a week ?

1. 1. 10	5	days
      	24

   
   
   

   2. 4	4	days
      	5

   
   
   

   3. 6	8	days
      	15

   
   
   

   4. 12	6	days
      	19

   
   
   

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1. View Hint View Answer Discuss in Forum

   A’s 4 days’ work = B’s 5 days’ work
   ⇒ A : B = 4 : 5
   Again, B : C = 6 : 7
   ∴ A : B : C = 4 × 6 : 5 × 6 : 5 × 7 = 24 : 30 : 35
   ∵ Time taken by A = 7 days
   

   ∴ Time taken by C =	35	× 7
   	24

   
   

   =	245	= 10	5	days
   	24		24

   Correct Option: A

   A’s 4 days’ work = B’s 5 days’ work
   ⇒ A : B = 4 : 5
   Again, B : C = 6 : 7
   ∴ A : B : C = 4 × 6 : 5 × 6 : 5 × 7 = 24 : 30 : 35
   ∵ Time taken by A = 7 days
   

   ∴ Time taken by C =	35	× 7
   	24

   
   

   =	245	= 10	5	days
   	24		24

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49. A and B can do a piece of work in 18 days, B and C in 24 days, A and C in 36 days. Working together they can do the work in

1. 1. 12 days

   
   
   

   2. 13 days

   
   
   

   3. 16 days

   
   
   

   4. 26 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   (A + B)’s 1 day’s work =	1
   	18

   
   

   (B + C)’s 1 day’s work =	1
   	24

   
   

   (C + A)’s 1 day’s work =	1
   	36

   
   On adding all three,
   2 (A + B + C)’s 1 day’s work
   

   =	1	+	1	+	1	=	3 + 4 + 2
   	18		24		36		72

   
   

   =	9	=	1
   	72		8

   
   ∴ (A + B + C)’s 1 day’s work
   

   =	1
   	16

   
   ∴ Required time = 16 days

   Correct Option: C

   (A + B)’s 1 day’s work =	1
   	18

   
   

   (B + C)’s 1 day’s work =	1
   	24

   
   

   (C + A)’s 1 day’s work =	1
   	36

   
   On adding all three,
   2 (A + B + C)’s 1 day’s work
   

   =	1	+	1	+	1	=	3 + 4 + 2
   	18		24		36		72

   
   

   =	9	=	1
   	72		8

   
   ∴ (A + B + C)’s 1 day’s work
   

   =	1
   	16

   
   ∴ Required time = 16 days

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50. A canal of a village can be cleaned by 24 villagers in 12 days. The number of days in which 36 villagers can clean the canal is

1. 1. 18

   
   
   

   2. 8

   
   
   

   3. 72

   
   
   

   4. 16

   
   
   

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1. View Hint View Answer Discuss in Forum

   M₁D₁ = M₂D₂
   ⇒ 24 × 12 = 36 × D₂
   

   ⇒ D2 =	24 × 12	= 8 days
   	36

   Correct Option: B

   M₁D₁ = M₂D₂
   ⇒ 24 × 12 = 36 × D₂
   

   ⇒ D2 =	24 × 12	= 8 days
   	36

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