76. If 6 men and 8 boys can do a piece of work in 10 days and 26 men and 48 boys can do the same in 2 days, then the time taken by 15 men and 20 boys to do the same type of work will be :

1. 1. 5 days

   
   
   

   2. 4 days

   
   
   

   3. 6 days

   
   
   

   4. 7 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to question,
   (6M + 8B) × 10 = (26M + 48B) × 2
   ∴ 60M + 80B = 52M + 96B
   or, 1M = 2B
   ∴ 15M + 20B = (30 + 20)B
   = 50 boys and 6M + 8B
   = (12 + 8) boys = 20 boys
   ∵ 20 boys can finish the work in 10 days
   ∴ 50 boys can finish the work in
   

   	20 × 10	days = 4 days
   	50

   
   Aliter : Using Rule 11,
   A₁ = 6, B₁ = 8, D₁ = 10
   A₂ = 26, B₂ = 48, D₂ = 2
   A₃ = 15, B₃ = 20
   Required time
   

   =	D1D2(A1B2 - B1A2	days
   	D1(A1B3 - A3B1) - D2(A2B3 - A3B2)

   
   

   =	10 × 2(6 × 48 - 8 × 26)	days
   	10(6 × 20 - 15 × 8) - 2(26 × 20 - 15 × 48)

   
   

   =	20(288 - 208)
   	10(120 - 120) - 2(520 - 720)

   
   

   =	20 × 80	= 4 days
   	400

   Correct Option: B

   According to question,
   (6M + 8B) × 10 = (26M + 48B) × 2
   ∴ 60M + 80B = 52M + 96B
   or, 1M = 2B
   ∴ 15M + 20B = (30 + 20)B
   = 50 boys and 6M + 8B
   = (12 + 8) boys = 20 boys
   ∵ 20 boys can finish the work in 10 days
   ∴ 50 boys can finish the work in
   

   	20 × 10	days = 4 days
   	50

   
   Aliter : Using Rule 11,
   A₁ = 6, B₁ = 8, D₁ = 10
   A₂ = 26, B₂ = 48, D₂ = 2
   A₃ = 15, B₃ = 20
   Required time
   

   =	D1D2(A1B2 - B1A2	days
   	D1(A1B3 - A3B1) - D2(A2B3 - A3B2)

   
   

   =	10 × 2(6 × 48 - 8 × 26)	days
   	10(6 × 20 - 15 × 8) - 2(26 × 20 - 15 × 48)

   
   

   =	20(288 - 208)
   	10(120 - 120) - 2(520 - 720)

   
   

   =	20 × 80	= 4 days
   	400

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77. A and B together can complete a piece of work in 12 days. They worked together for 5 days and then A alone finished the rest of the work in 14 days. A alone can complete the work in

1. 1. 24 days

   
   
   

   2. 22 days

   
   
   

   3. 20 days

   
   
   

   4. 18 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   ∵ (A + B)’s 1 day’s work =	1
   	12

   
   

   ∴ (A + B)’s 5 days’ work =	5
   	12

   
   

   Remaining work = 1 –	5	=	7
   	12		12

   
   

   ∵ A does	7	work in 14 days
   	12

   
   

   ∴ A will do 1 work in =	14 × 12	= 24 days;
   	7

   Correct Option: A

   ∵ (A + B)’s 1 day’s work =	1
   	12

   
   

   ∴ (A + B)’s 5 days’ work =	5
   	12

   
   

   Remaining work = 1 –	5	=	7
   	12		12

   
   

   ∵ A does	7	work in 14 days
   	12

   
   

   ∴ A will do 1 work in =	14 × 12	= 24 days;
   	7

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78. A can do a work in 15 days and B in 20 days.If they together work on it for 4 days, then the fraction of the work that is left is:

1. 1. 8

      15

   
   
   

   2. 7

      15

   
   
   

   3. 1

      4

   
   
   

   4. 1

      10

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using basics of Rule 2,
   

   A’s work per da =	1
   	15

   
   

   B’s work per day =	1
   	20

   
   (A+ B)’s work per day
   

   =	1	+	1	=	4 + 3	=	1
   	15		20		60		60

   
   ∴ (A + B)’s work in 4 days
   

   = 4 ×	7	=	7
   	60		15

   
   

   Left work = 1 -	7
   	15

   
   

   =	15 - 7	=	8
   	15		15

   Correct Option: A

   Using basics of Rule 2,
   

   A’s work per da =	1
   	15

   
   

   B’s work per day =	1
   	20

   
   (A+ B)’s work per day
   

   =	1	+	1	=	4 + 3	=	1
   	15		20		60		60

   
   ∴ (A + B)’s work in 4 days
   

   = 4 ×	7	=	7
   	60		15

   
   

   Left work = 1 -	7
   	15

   
   

   =	15 - 7	=	8
   	15		15

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79. A and B can do a piece of work in 72 days, B and C can do it in 120 days, and A and C can do it in 90 days. When A, B and C work together, how much work is finished by them in 3 days.

1. 1. 1

      40

   
   
   

   2. 1

      30

   
   
   

   3. 1

      20

   
   
   

   4. 1

      10

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using basics of Rule 5,
   

   (A + B)’s 1 day’s work =	1
   	72

   
   

   (B + C)’s 1 day’s work =	1
   	120

   
   

   (C + A)’s 1 day’s work =	1
   	90

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

   =	1	+	1	+	1
   	72		120		90

   
   

   =	5 + 3 + 4	=	1
   	360		30

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

   =	1
   	60

   
   ∴ (A + B + C)’s 3 days’ work
   

   =	3	=	1
   	60		20

   Correct Option: C

   Using basics of Rule 5,
   

   (A + B)’s 1 day’s work =	1
   	72

   
   

   (B + C)’s 1 day’s work =	1
   	120

   
   

   (C + A)’s 1 day’s work =	1
   	90

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

   =	1	+	1	+	1
   	72		120		90

   
   

   =	5 + 3 + 4	=	1
   	360		30

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

   =	1
   	60

   
   ∴ (A + B + C)’s 3 days’ work
   

   =	3	=	1
   	60		20

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80. P can complete 1/4 of a work in 10 days, Q can complete 40% of the same work in 15 days, R, completes 1/3 of the work in 13 days and S, 1/6 of the work in 7 days. Who will be able to complete the work first ?

1. 1. P

   
   
   

   2. Q

   
   
   

   3. R

   
   
   

   4. S

   
   
   

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1. View Hint View Answer Discuss in Forum

   Time taken by P in completing 1 work = 10 × 4 = 40 days
   Time taken by Q in completing 1 work
   

   =	15 × 5	=	75	days
   	2		2

   
   Time taken by R in completing 1
   work = 13 × 3 = 39 days
   Time taken by S in completing 1
   work = 7 × 6 = 42 days
   Clearly, Q took the least time i.e.
   

   	75	or 37	1	days
   	2		2

   Correct Option: B

   Time taken by P in completing 1 work = 10 × 4 = 40 days
   Time taken by Q in completing 1 work
   

   =	15 × 5	=	75	days
   	2		2

   
   Time taken by R in completing 1
   work = 13 × 3 = 39 days
   Time taken by S in completing 1
   work = 7 × 6 = 42 days
   Clearly, Q took the least time i.e.
   

   	75	or 37	1	days
   	2		2

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