Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 14 Jun 2011
Posts: 15

Jane and Ashley take 20 days and 40 days respectively to
[#permalink]
Show Tags
27 Dec 2012, 13:36
Question Stats:
54% (02:33) correct 46% (02:55) wrong based on 249 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10634
Location: Pune, India

Re: Jane and Ashley take 20 days and 40 days respectively to
[#permalink]
Show Tags
31 Jan 2013, 20:39
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 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
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




VP
Joined: 02 Jul 2012
Posts: 1091
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: Jane and Ashley take 20 days and 40 days respectively to
[#permalink]
Show Tags
31 Jan 2013, 20:51
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




Director
Joined: 17 Dec 2012
Posts: 631
Location: India

Re: Jane and Ashley take 20 days and 40 days respectively to
[#permalink]
Show Tags
Updated on: 27 Dec 2012, 17:04
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.
_________________
Srinivasan Vaidyaraman Magical LogiciansHolistic and Holy Approach



Manager
Joined: 03 Nov 2009
Posts: 54

Re: Jane and Ashley take 20 days and 40 days respectively to
[#permalink]
Show Tags
27 Dec 2012, 16:06
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 (158)*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



Intern
Joined: 25 Sep 2012
Posts: 11

Re: Jane and Ashley take 20 days and 40 days respectively to
[#permalink]
Show Tags
31 Jan 2013, 19:47
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 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. How could you reach to 4/5th of the total work please explain in detail



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2799

Re: Jane and Ashley take 20 days and 40 days respectively to
[#permalink]
Show Tags
03 May 2018, 15:24
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 Jane’s rate is 1/20, Ashley’s rate is 1/40, and their combined rate is 1/20 + 1/40 = 2/40 + 1/40 = 3/40. We can let n = the number of days they actually worked together and create the equation: Together + Ashley alone + Jane alone = 1 job (3/40)n + (1/40)8 + (1/20)4 = 1 3n/40 + 8/40 + 4/20 = 1 Multiplying by 40 we have: 3n + 8 + 8 = 40 3n = 24 n = 8 So it took 8 + 8 + 4 = 20 days to complete the project. Answer: E
_________________
5star rated online GMAT quant self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews



Manager
Joined: 09 Nov 2015
Posts: 205

Jane and Ashley take 20 days and 40 days respectively to
[#permalink]
Show Tags
18 Jun 2019, 06:40
We are told that Jane had to work FOUR extra days to make up for the workloss incurred because of the EIGHT days leave that she took while working together with Ashley.We can thus conclude that, while determining how many days they would need to complete the project (Scheduled Time for Completion or STC), Jane and Ashley had factored in a fourday leave for Jane. If we denote STC by 'x', the plan was that Jane would work for (x4) days and Ashley 'x' days. So as per the STC, Jane would have done (1/20)*(x4)th of the work and Ashley (1/40)*(x)th.
(1/20)*(x4) + (1/40)*x = 1....> x=16
Scheduled time for completion of project = 16 days Actual time taken to complete project = 16+4=20 days. ANS: E




Jane and Ashley take 20 days and 40 days respectively to
[#permalink]
18 Jun 2019, 06:40




