Jane and Ashley take 20 days and 40 days respectively to

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Jane and Ashley take 20 days and 40 days respectively to [#permalink]

27 Dec 2012, 14:36

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Jane and Ashley take 20 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ?

(A) 10 Days
(B) 15 Days
(C) 16 Days
(D) 18 Days
(E) 20 Days

[Reveal] Spoiler: OA

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Re: Jane and Ashley take 20 days and 40 days respectively to [#permalink]

27 Dec 2012, 15:57

tabsang wrote:

Jane and Ashley take 20 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it.
During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ?

(A) 10 Days
(B) 15 Days
(C) 16 Days
(D) 18 Days
(E) 20 Days

Assume Jane and Ashley worked together for x days without considering the 8 day leave of Jane. They would have completed x(\frac{1}{40} + \frac{1}{20}) of the total work in those days. In the period when Jane took a 8 day leave, Ashley worked alone. So Ashley worked alone for 8 days. He would have completed \frac{8}{40} th of the total work. The work finished before Jane started working alone, is x(\frac{1}{20} + \frac{1}{40}) + \frac{8}{40}. This is equal to \frac{4}{5} of the total work as in the period when Jane was working alone which is 4 days, she would have completed \frac{4}{20} or \frac{1}{5} of the work. Previously done work is therefore \frac{4}{5}.

x(\frac{1}{40} +\frac{1}{20}) +\frac{8}{40} = \frac{4}{5}

We have x = 8

Add to this the 8 days when Ashley worked alone and the 4 days when Jane worked alone. The total is 8+8+4=20 days.
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Last edited by SravnaTestPrep on 27 Dec 2012, 18:04, edited 2 times in total.

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Re: Jane and Ashley take 20 days and 40 days respectively to [#permalink]

27 Dec 2012, 17:06

I generally use take a constant (LCM) and a production example for this kind of questions.

Assuming that Jane and Ashley's work is production of certain number of Toys

In 20 days Jane completes making certain number of Toys and the same number of Toys takes 40 days for Ashley to complete, so we take the LCM (Lowest common Multiple) which would be the target work = 80 toys to complete

From above assumption we know that Jane completes 4 toys / day as in 80/20 days

And Ashley completes 2 toys / Day as in 80/40 days

Now if both worked without any break they would take 80/4+2 days to complete which is 13.333 days, so that eliminates choice (A) = 10 days

Now plugging in choices, B - Jane completes (15-8)*4 = 28
Ashley completes 15*2 =30
Total work in 15 days with 8 days break by Jane = 28+30 = 58 toys
Jane works for 4 days on her own = 4*4 = 16 toys
So in 15 days ( both Jane & Ashley)+ 4 days(only Jane) they complete 58+16 =74 toys, 6 short of the target of 80

Plug in choice C - Ashley completes 16*2= 32 toys
Jane completes 8*4 = 32 toys
Total in 16 days = 64 toys
Jane takes 4 days on her own, 4*4 = 16 toys
So in 16 days ( both Jane & Ashley)+ 4 days(only Jane) they complete = 64+16 = 80 toys which is the target.

Ans : E

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Re: Jane and Ashley take 20 days and 40 days respectively to [#permalink]

31 Jan 2013, 20:47

SravnaTestPrep wrote:

tabsang wrote:

Jane and Ashley take 20 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it.
During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ?

(A) 10 Days
(B) 15 Days
(C) 16 Days
(D) 18 Days
(E) 20 Days

How could you reach to 4/5th of the total work please explain in detail

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Re: Jane and Ashley take 20 days and 40 days respectively to [#permalink]

31 Jan 2013, 21:39

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tabsang wrote:

Remember, Work = Rate*Time and Rate = 1/Time

Ashley worked alone on the project for 8 days. Work done in these 8 days = R*T = (1/40)*8 = 1/5
Jane worked alone on the project for 4 days. Work done in these 4 days = R*T = (1/20)*4 = 1/5
Leftover work = 1 - 1/5 - 1/5 = 3/5

On this 3/5 work, both worked together. Their combined rate = 1/20 + 1/40 = 3/40
3/5 = 3/40*T
T = 8 days

Total time taken = 8 (Ashley worked alone) + 4(Jane worked alone) + 8 (Both worked together) = 20 days
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Re: Jane and Ashley take 20 days and 40 days respectively to [#permalink]

31 Jan 2013, 21:51

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Let us assume that the work is laying 40 bricks.

Jane = 2 bricks per day
Ashley = 1 brick per day
Together = 3 bricks per day

Let's say first 8 days Ashley works alone,
No of bricks = 8
Last 4 days Jane works alone,
No. of bricks = 8

Remaining bricks = 40 - 16 = 24
So together, they would take 24/3 = 8

Total no. of days = 8 + 4 + 8 = 20

Answer is E
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Re: Jane and Ashley take 20 days and 40 days respectively to [#permalink] 31 Jan 2013, 21:51

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