31. A certain number of persons can complete a piece of work in 55 days. If there were 6 persons more, the work could be finished in 11 days less. How many persons were originally there ?

1. 1. 17

   
   
   

   2. 24

   
   
   

   3. 30

   
   
   

   4. 22

   
   
   

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1. View Hint View Answer Discuss in Forum

   Originally, let there be x men
   Now, more men, less days
   (x + 6) : x : : 55 : 44
   

   So,	x + 6	=	55	=	5
   	x		44		4

   
   or 5x = 4x + 24
   or x = 24
   Aliter : Using Rule 23,
   Here, D = 55. a = 6, d = 11
   No of people initially
   

   =	a(D - d)
   	d

   
   

   =	6(55 - 11)	= 24
   	11

   Correct Option: B

   Originally, let there be x men
   Now, more men, less days
   (x + 6) : x : : 55 : 44
   

   So,	x + 6	=	55	=	5
   	x		44		4

   
   or 5x = 4x + 24
   or x = 24
   Aliter : Using Rule 23,
   Here, D = 55. a = 6, d = 11
   No of people initially
   

   =	a(D - d)
   	d

   
   

   =	6(55 - 11)	= 24
   	11

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32. A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in :

1. 1. 5 days

   
   
   

   2. 6 days

   
   
   

   3. 10 days

   
   
   

   4. 10	1	days
      	2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Work done by (B + C) in 3 days.
   

   = 3 ×		1	+	1
   		9		12

   
   

   =	1	+	1	=	4 + 3	=	7
   	3		4		12		12

   
   

   Remaining work = 1 -	7	=	5
   	12		12

   
   This part of work is done by A alone.
   

   Now,	1	part of work is done by A in 1 day
   	24

   
   

   ∴	5	part of work will be done by
   	12

   
   

   A in = 24 ×	5	= 10 days.
   	12

   Correct Option: C

   Work done by (B + C) in 3 days.
   

   = 3 ×		1	+	1
   		9		12

   
   

   =	1	+	1	=	4 + 3	=	7
   	3		4		12		12

   
   

   Remaining work = 1 -	7	=	5
   	12		12

   
   This part of work is done by A alone.
   

   Now,	1	part of work is done by A in 1 day
   	24

   
   

   ∴	5	part of work will be done by
   	12

   
   

   A in = 24 ×	5	= 10 days.
   	12

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33. 8 men can do a work in 12 days. After 6 days of work, 4 more men were engaged to finish the work. In how many days would the remaining work be completed?

1. 1. 2

   
   
   

   2. 3

   
   
   

   3. 4

   
   
   

   4. 5

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   Work done by 8 men in 6 days
   

   =	6	=	1
   	12		2

   
   

   Remaining work = 1 -	1	=	1
   	2		2

   
   4 more men are engaged.
   ∴ Total number of men
   = 8 + 4 = 12
   By work and time formula
   

   	W1	=	W2	, we have
   	M1D1		M2D2

   
   

   	1	=	1/2
   	8 × 12		12 × D2

   
   

   ⇒ D2 =	1	×	8 × 12	= 4 days
   	2		12

   Correct Option: C

   Using Rule 1,
   Work done by 8 men in 6 days
   

   =	6	=	1
   	12		2

   
   

   Remaining work = 1 -	1	=	1
   	2		2

   
   4 more men are engaged.
   ∴ Total number of men
   = 8 + 4 = 12
   By work and time formula
   

   	W1	=	W2	, we have
   	M1D1		M2D2

   
   

   	1	=	1/2
   	8 × 12		12 × D2

   
   

   ⇒ D2 =	1	×	8 × 12	= 4 days
   	2		12

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34. A and B can together finish a work in 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the job ?

1. 1. 50 days

   
   
   

   2. 60 days

   
   
   

   3. 48 days

   
   
   

   4. 54 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   (A+B)’s 1 day’s work =	1
   	30

   
   

   (A + B)’s 20 day’s work =	20	=	2
   	30		3

   
   

   Remaining work = 1 -	2	=	1
   	3		3

   
   

   Now	1	part of work is done by A in 20 days
   	3

   
   ∴ Whole work will be done by A alone in 20 × 3 = 60 days.

   Correct Option: B

   (A+B)’s 1 day’s work =	1
   	30

   
   

   (A + B)’s 20 day’s work =	20	=	2
   	30		3

   
   

   Remaining work = 1 -	2	=	1
   	3		3

   
   

   Now	1	part of work is done by A in 20 days
   	3

   
   ∴ Whole work will be done by A alone in 20 × 3 = 60 days.

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35. A and B can do a piece of work in 30 days while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work ?

1. 1. 18 days

   
   
   

   2. 24 days

   
   
   

   3. 30 days

   
   
   

   4. 36 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   (A + B)’s day’s work =	1
   	30

   
   

   (B + C)’s 1 day’s work =	1
   	24

   
   

   (C + A)’s 1 day’s work =	1
   	20

   
   ∴ 2 (A + B + C)’s 1 day’s work
   

   =	1	+	1	+	1
   	30		24		20

   
   

   =	4 + 5 + 6	=	15	=	1
   	120		120		8

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

   =	1
   	16

   
   ∴ (A + B + C)’s 10 days’ work
   

   =	10	=	5
   	16		8

   
   

   ∴ Remaining work = 1 -	5	=	3
   	8		8

   
   This part of work is done by A alone.
   

   Now A’s 1 day’s work =	1	-	1
   	16		24

   
   

   =	3 - 2	=	1
   	48		48

   
   ∴ The required no. of days
   

   =	3	× 48 = 18 days
   	8

   Correct Option: A

   (A + B)’s day’s work =	1
   	30

   
   

   (B + C)’s 1 day’s work =	1
   	24

   
   

   (C + A)’s 1 day’s work =	1
   	20

   
   ∴ 2 (A + B + C)’s 1 day’s work
   

   =	1	+	1	+	1
   	30		24		20

   
   

   =	4 + 5 + 6	=	15	=	1
   	120		120		8

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

   =	1
   	16

   
   ∴ (A + B + C)’s 10 days’ work
   

   =	10	=	5
   	16		8

   
   

   ∴ Remaining work = 1 -	5	=	3
   	8		8

   
   This part of work is done by A alone.
   

   Now A’s 1 day’s work =	1	-	1
   	16		24

   
   

   =	3 - 2	=	1
   	48		48

   
   ∴ The required no. of days
   

   =	3	× 48 = 18 days
   	8

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