126. A can do a work in 12 days. When he had worked for 3 days, B joined him. If they complete the work in 3 more days, in how many days can B alone finish the work?

1. 1. 6 days

   
   
   

   2. 12 days

   
   
   

   3. 4 days

   
   
   

   4. 8 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let B alone do the work in x days.
   

   ∴ 6 ×	1	+ 3 ×	1	= 1
   	12		x

   
   

   ⇒	1	+	3	= 1
   	2		x

   
   

   ⇒	3	=	1	⇒ x = 6 days
   	x		2

   Correct Option: A

   Let B alone do the work in x days.
   

   ∴ 6 ×	1	+ 3 ×	1	= 1
   	12		x

   
   

   ⇒	1	+	3	= 1
   	2		x

   
   

   ⇒	3	=	1	⇒ x = 6 days
   	x		2

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127. A road of 5 km length will be constructed in 100 days. So 280 workers were employed. But after 80 days it was found that only
     

     3	1	km road was completed.
     	2

     
     Now how many more people were needed to finish the work in the specified time ?

1. 1. 480

   
   
   

   2. 80

   
   
   

   3. 200

   
   
   

   4. 100

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   Remaining work
   

   = 5 –	7	=	3
   	2		2

   
   M₁ × D₁ × W₂ = M₂ × D₂ × W₁
   

   ⇒ 280 × 80 ×	3
   	2

   
   

   = M2 × 20 ×	7
   	2

   
   

   ⇒ M2 =	280 × 80 × 3	= 480
   	20 × 7

   
   ∴ Required number of additional men = 480 – 280 = 200

   Correct Option: C

   Using Rule 1,
   Remaining work
   

   = 5 –	7	=	3
   	2		2

   
   M₁ × D₁ × W₂ = M₂ × D₂ × W₁
   

   ⇒ 280 × 80 ×	3
   	2

   
   

   = M2 × 20 ×	7
   	2

   
   

   ⇒ M2 =	280 × 80 × 3	= 480
   	20 × 7

   
   ∴ Required number of additional men = 480 – 280 = 200

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128. Ganga and Saraswati, working separately can mow a field in 8 and 12 hours respectively. If they work in stretches of one hour alternately, Ganga beginning at 9 a.m., when will the moving be completed ?

1. 1. 6 p.m.

   
   
   

   2. 6.30 p.m.

   
   
   

   3. 5 p.m.

   
   
   

   4. 5.30 p.m.

   
   
   

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1. View Hint View Answer Discuss in Forum

   Part of the field mowed by
   Ganga and Saraswati in first 2 hours
   

   =	1	+	1	=	3 + 2	=	5
   	8		12		24		24

   
   ∴ Part of the field mowed in first 8 hours
   

   =	5 × 4	=	20	=	5
   	24		24		6

   
   Remaining work
   

   = 1 -	5	=	1
   	6		6

   
   Now, it is the turn of Ganga, part of work done by Ganga in 1 hour
   

   =	1
   	8

   
   Remaining work
   

   =	1	-	1
   	6		8

   
   

   =	4 - 3	=	1
   	24		24

   
   Now, time taken by Saraswati in completing this part of work
   

   =	1	× 12 =	1	hour
   	24		2

   
   

   ∴ Total time = 9	1	hours
   	2

   
   The mowing starts at 9 am.
   Hence, the mowing will be completed at 6.30 pm.

   Correct Option: B

   Part of the field mowed by
   Ganga and Saraswati in first 2 hours
   

   =	1	+	1	=	3 + 2	=	5
   	8		12		24		24

   
   ∴ Part of the field mowed in first 8 hours
   

   =	5 × 4	=	20	=	5
   	24		24		6

   
   Remaining work
   

   = 1 -	5	=	1
   	6		6

   
   Now, it is the turn of Ganga, part of work done by Ganga in 1 hour
   

   =	1
   	8

   
   Remaining work
   

   =	1	-	1
   	6		8

   
   

   =	4 - 3	=	1
   	24		24

   
   Now, time taken by Saraswati in completing this part of work
   

   =	1	× 12 =	1	hour
   	24		2

   
   

   ∴ Total time = 9	1	hours
   	2

   
   The mowing starts at 9 am.
   Hence, the mowing will be completed at 6.30 pm.

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129. If two persons, with equal abilities, can do two jobs in two days, then 100 persons with equal abilities can do 100 similar jobs in

1. 1. 100 days

   
   
   

   2. 10 days

   
   
   

   3. 5 days

   
   
   

   4. 2 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to the question,
   2 persons with equal abilities can do 1 job in 1 day
   ∴ Time taken by 1 man to complete 1 job = 2 days
   ⇒ Time taken by 100 persons in completing 100 jobs = 2 days

   Correct Option: D

   According to the question,
   2 persons with equal abilities can do 1 job in 1 day
   ∴ Time taken by 1 man to complete 1 job = 2 days
   ⇒ Time taken by 100 persons in completing 100 jobs = 2 days

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130. 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 for 10 days when B and C leave.
     How many days more will A take to complete the work?

1. 1. 16 days

   
   
   

   2. 15 days

   
   
   

   3. 18 days

   
   
   

   4. 20 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 3,
   

   (A + B)’s 1 day’s work =	1
   	30

   
   

   (B + C)’s 1 day’s work =	1
   	24

   
   

   (C + A)’s 1 day’s work =	1
   	20

   
   Adding all the above, we have
   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	=	1
   	8 × 2		16

   
   Now, all three worked together for 10 days.
   ∴ (A + B + C)’s 10 days’ work
   

   =	1	× 10 =	5
   	16		8

   
   ∴ Remaining part of work
   

   = 1 -	5	=	8 - 5	=	3
   	8		8		8

   
   Now, A’s 1 day’s work
   

   =	1	-	1	=	3 - 2	=	1
   	16		24		48		48

   
   Since, A finishes 1/48 part of work in 1 day
   ∴ A will finish 3/8 part of work in
   

   1 × 48 ×	3	= 18 days.
   	8

   Correct Option: C

   Using Rule 3,
   

   (A + B)’s 1 day’s work =	1
   	30

   
   

   (B + C)’s 1 day’s work =	1
   	24

   
   

   (C + A)’s 1 day’s work =	1
   	20

   
   Adding all the above, we have
   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	=	1
   	8 × 2		16

   
   Now, all three worked together for 10 days.
   ∴ (A + B + C)’s 10 days’ work
   

   =	1	× 10 =	5
   	16		8

   
   ∴ Remaining part of work
   

   = 1 -	5	=	8 - 5	=	3
   	8		8		8

   
   Now, A’s 1 day’s work
   

   =	1	-	1	=	3 - 2	=	1
   	16		24		48		48

   
   Since, A finishes 1/48 part of work in 1 day
   ∴ A will finish 3/8 part of work in
   

   1 × 48 ×	3	= 18 days.
   	8

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