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A is 1.5 times as fast as B. A alone can do the work in 20 days. If A

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A is 1.5 times as fast as B. A alone can do the work in 20 days. If A [#permalink]

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New post 19 Feb 2016, 23:22
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Question Stats:

74% (01:54) correct 26% (01:25) wrong based on 112 sessions

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A is 1.5 times as fast as B. A alone can do the work in 20 days. If A and B work on alternative days, beginning with A, in how many days will the work be completed?

A) 23
B) 22
C) 21
D) 24
E) 25

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Re: A is 1.5 times as fast as B. A alone can do the work in 20 days. If A [#permalink]

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New post 20 Feb 2016, 00:14
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A can do the work in 20 days = 100/20 =5% of the work can be completed in 1 day by A
B can do the work in 1.5*20 = 30 days (100/30) =3.33% of the work can be completed in 1 day by B.
Starting alternatively from A and B (Combined work = 5+3.33 = 8.33%) of the work can be completed in 2 days.
Therefore, 100/8.33 = 12 (which means 12*2 = 24 days)

Hence D is the answer.
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A is 1.5 times as fast as B. A alone can do the work in 20 days. If A [#permalink]

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New post 21 Feb 2016, 01:09
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A can finish 1 work in 20 days
B can finish 1/1.5 work in 20 days - since A is 1.5 faster than B

This means
B can finish 1 work in 20*1.5 days = 30 days

Now using the awesome GMAT formula when two machines work together they can finish the job in = AB/ (A+B) = 20*30/(20+30) = 20*30/50 = 12 days

Since they alternate on days, it will take them double this time so total time = 12 * 2 = 24 days

So answer is D
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Re: A is 1.5 times as fast as B. A alone can do the work in 20 days. If A [#permalink]

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New post 25 Feb 2016, 17:28
Mesto wrote:
A is 1.5 times as fast as B. A alone can do the work in 20 days. If A and B work on alternative days, beginning with A, in how many days will the work be completed?

A) 23
B) 22
C) 21
D) 24
E) 25


Time taken by A - 20 days
A - Rate = 1/20 to complete 1 job.

B rate is 1/(20*1.5) = 1/30

Total number of days taken by both of them together working alternatively= X

Work-Time equation
X/(2*20) + X/(2*30) = 1

Solving, X=24
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Re: A is 1.5 times as fast as B. A alone can do the work in 20 days. If A [#permalink]

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New post 04 May 2016, 19:46
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Mesto wrote:
A is 1.5 times as fast as B. A alone can do the work in 20 days. If A and B work on alternative days, beginning with A, in how many days will the work be completed?

A) 23
B) 22
C) 21
D) 24
E) 25


1/20 = 1/A
1/A = 1.5/B
B must be 1/30

i found it easy to set a task consisting of 60 units.
A does 3 units per day, B does 2 units per day. in 2 days, A and B get done 5 units of work. since we need a 60/5 = 12 series of alternative days, the task will be completed in 12*2=24 days.
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Re: A is 1.5 times as fast as B. A alone can do the work in 20 days. If A [#permalink]

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New post 04 May 2016, 20:49
Mesto wrote:
A is 1.5 times as fast as B. A alone can do the work in 20 days. If A and B work on alternative days, beginning with A, in how many days will the work be completed?

A) 23
B) 22
C) 21
D) 24
E) 25


Using ratios can help too.
Ratio of speed = 1.5:1= 3:2
Ratio of time taken = 2:3
So B alone takes 30 days
Together, working alternate days, the two of them complete 1/20 + 1/30 = 5/60 of the work every 2 days.
So they take (60/5 = 12)*2 = 24 days to complete the work.

Answer (D)
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Re: A is 1.5 times as fast as B. A alone can do the work in 20 days. If A [#permalink]

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New post 25 Apr 2017, 06:44
A's rate = 1/20
B's rate = 1/(20*1.5) = 1/30
The alternative time is the double of the time for A & B together
(1/20 + 1/30) * (1/2 T) = 1
T/20 = 6/5
T=24
Re: A is 1.5 times as fast as B. A alone can do the work in 20 days. If A   [#permalink] 25 Apr 2017, 06:44
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