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A and B working separately can do a piece of work in 9 and 12 days res

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A and B working separately can do a piece of work in 9 and 12 days res  [#permalink]

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New post 30 Jan 2019, 02:06
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A and B working separately can do a piece of work in 9 and 12 days respectively.If they work for a day alternately, A beginning, in how many days, the work will be completed?


A. \(10 \frac{1}{5}\)

B. \(10 \frac{1}{4}\)

C. \(10 \frac{1}{3}\)

D. \(10 \frac{1}{2}\)

E. \(10 \frac{2}{3}\)

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Re: A and B working separately can do a piece of work in 9 and 12 days res  [#permalink]

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New post 30 Jan 2019, 02:24
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Total work to be done = LCM(9,12) = 36 units.

A can do 4 units per day
B can do 3 units per day

In 2 days, A and B can do 7 units.
In 10 days, 35 unit will be completed.
Remaining is 1 unit and A will do it in 1/4 days.

\(10\frac{1}{4}\) is the answer.

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Re: A and B working separately can do a piece of work in 9 and 12 days res  [#permalink]

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New post 30 Jan 2019, 02:51
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Bunuel wrote:
A and B working separately can do a piece of work in 9 and 12 days respectively.If they work for a day alternately, A beginning, in how many days, the work will be completed?


A. \(10 \frac{1}{5}\)

B. \(10 \frac{1}{4}\)

C. \(10 \frac{1}{3}\)

D. \(10 \frac{1}{2}\)

E. \(10 \frac{2}{3}\)


Combining both works of A & B given rate 1/9 & 1/12 ; LCM = 36

so days taken by A = 36/9= 4 and B 36/12= 3 days
avg time = 4+3/2 = 3.5

so in 10 days 3.5*10 = 35 days work done done
left with 36-35= 1 day work
which A can do as its rate is 1/4

IMO B \(10 \frac{1}{4}\)
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Re: A and B working separately can do a piece of work in 9 and 12 days res  [#permalink]

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New post 01 Feb 2019, 18:07
Bunuel wrote:
A and B working separately can do a piece of work in 9 and 12 days respectively.If they work for a day alternately, A beginning, in how many days, the work will be completed?


A. \(10 \frac{1}{5}\)

B. \(10 \frac{1}{4}\)

C. \(10 \frac{1}{3}\)

D. \(10 \frac{1}{2}\)

E. \(10 \frac{2}{3}\)


We see that A’s rate = 1/9, and B’s rate = 1/12. Since A starts first, A works one more day than B. So if we let x = the number of days B works, then x + 1 = the number of days A works. We can create the equation:

(1/9)(x + 1) + (1/12)x = 1

Multiplying both sides by 36, we have:

4(x + 1) + 3x = 36

4x + 4 + 3x = 36

7x = 32

x = 32/7 = 4 4/7

We see that x is not a whole number. If we round x up to 5, then certainly the two workers will be “overworked.” That is, the amount they work together will exceed 1 job. Therefore, we have to round x down to 4. That is, B works 4 days and A works 5 days. They will now be “underworked,” but we can figure out how much time will be needed for the remainder of the job. So if B works 4 days and A works 5 days, together they have completed 4(1/12) + 5(1/9) = 1/3 + 5/9 = 8/9 of the job. If the remaining 1/9 of the job will be completed by B for one more day, then 1/9 - 1/12 = 1/36 of the job still needs to be completed and that fraction of the job can be completed by A in (1/36)/(1/9) = 9/36 = 1/4 of a day. Therefore, in total, they work 4 + 5 + 1 + 1/4 = 10 1/4 days.

Alternate Solution:

We can solve this problem by arithmetic. Let’s pair two days together: an “AB” pair is comprised of one day worked by A and the next day worked by B. The combined work in one AB pair is:

1/9 + 1/12 = 7/36 of the job.

Since the entire job is 1, or 36/36, we see that if we have 5 “AB” paired days (for a total of 10 days, 5 days worked by A and 5 worked by B), we will have finished 5 x 7/36, or 35/36, of the total job. Thus, we still have 1/36 of the job to complete. Since it is now A’s turn to work, we see that A can finish the remaining 1/36 of the job in (1/36)/(1/9) = 1/4 of a day. Thus, the total time for the job to be completed is 10 1/4 days.

Answer: B
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Re: A and B working separately can do a piece of work in 9 and 12 days res  [#permalink]

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New post 01 Feb 2019, 20:20
Bunuel wrote:
A and B working separately can do a piece of work in 9 and 12 days respectively.If they work for a day alternately, A beginning, in how many days, the work will be completed?


A. \(10 \frac{1}{5}\)

B. \(10 \frac{1}{4}\)

C. \(10 \frac{1}{3}\)

D. \(10 \frac{1}{2}\)

E. \(10 \frac{2}{3}\)


Let Work be 36 units, Now rate of A will be 4 units/day & Rate of B will be 3 units/day

If we start from A and then B follows

7 units of work will be done in 2 days
36 units will be done in 2/7 * 36 = 72/7 = 1.26

B when solved will give you the same value

B
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Re: A and B working separately can do a piece of work in 9 and 12 days res   [#permalink] 01 Feb 2019, 20:20
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