A quits before the project is completed

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed Feb 18, 2009 6:08 am

A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

A. 18 days
B. 27 days
C. 26.67 days
D. 16 days
E. 12 days

The mind is everything. What you think you become. -Lord Buddha

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Source: Beat The GMAT — Problem Solving | Wed Feb 18, 2009 6:08 am

billzhao: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Mon Feb 02, 2009 6:36 am; Thanked: 10 times

by billzhao » Wed Feb 18, 2009 7:02 am

Ra=1/20, Rb=1/30

(Ra+Rb)*(t-10)+Rb*10=1 =>

(1/20+1/30)*(t-10)+1/30*10=1

We can solve the equation for t.

t=18

Yiliang

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x2suresh: Master | Next Rank: 500 Posts; Posts: 258; Joined: Thu Aug 07, 2008 5:32 am; Thanked: 16 times

Re: A quits before the project is completed

by x2suresh » Wed Feb 18, 2009 7:35 am

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valdemas: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sat Jan 10, 2009 12:44 pm

Re: A quits before the project is completed

by valdemas » Wed Feb 18, 2009 8:59 am

x2suresh wrote:A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

A. 18 days
B. 27 days
C. 26.67 days
D. 16 days
E. 12 days
_________________

together they would take :

1/20+1/30 = 1/12 and that's equivalent to 12 days to do the job
this means that A quited after completing the second day...
so: A did 2/20 =1/10 of the job
B did 2/30 =1/15 of the job on the second day
together they did (1/10)+(1/15) = 1/6 of the job
if B takes 30 days to do 1 job; how much time would he take to do 1-(1/6) of the job?
R: 5/6 * 30= 25 days
so the full time = 25 days of B's work plus 2 days of (B+A)'s work = 27 days
the answer is B

n-10 (1/20 + 1/30)+10(1/30) =1

n-10 (50/600) = 2/3

n-10 = (2/3) * 12=8

n=18

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DarkKnight: Senior | Next Rank: 100 Posts; Posts: 79; Joined: Mon Sep 15, 2008 5:54 pm; Thanked: 3 times

by DarkKnight » Wed Feb 18, 2009 7:59 pm

Can you please post the OA?

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu Feb 19, 2009 2:02 am

DarkKnight wrote:Can you please post the OA?

B alone working for the last 10 days would finish 1/3 of the total work. This means that the unit (A & B) must have already completed 2/3 of the work at the rate of 1/12 part of work per day, which would have taken them to work for 8 days together. Thus the whole work was completed in 8 + 10 = 18 days; and that's the OA.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
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naaga: Master | Next Rank: 500 Posts; Posts: 129; Joined: Mon Dec 15, 2008 11:43 pm; Location: Hyderabad; Thanked: 2 times

by naaga » Fri Feb 20, 2009 5:42 am

sanju09 wrote:
DarkKnight wrote:Can you please post the OA?
B alone working for the last 10 days would finish 1/3 of the total work. This means that the unit (A & B) must have already completed 2/3 of the work at the rate of 1/12 part of work per day, which would have taken them to work for 8 days together. Thus the whole work was completed in 8 + 10 = 18 days; and that's the OA.

thanks buddy

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Jul 24, 2010 3:44 am

naaga wrote:
sanju09 wrote:
DarkKnight wrote:Can you please post the OA?
B alone working for the last 10 days would finish 1/3 of the total work. This means that the unit (A & B) must have already completed 2/3 of the work at the rate of 1/12 part of work per day, which would have taken them to work for 8 days together. Thus the whole work was completed in 8 + 10 = 18 days; and that's the OA.

thanks buddy

you are most welcome naaga baba

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
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The Princeton Review - Manya Abroad
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surfer123: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Mon Nov 01, 2010 6:30 pm; Thanked: 2 times

by surfer123 » Sun Dec 26, 2010 1:51 pm

what is wrong with the above logic

1/20+1/30 = 1/12 and that's equivalent to 12 days to do the job
this means that A quited after completing the second day...
so: A did 2/20 =1/10 of the job
B did 2/30 =1/15 of the job on the second day
together they did (1/10)+(1/15) = 1/6 of the job
if B takes 30 days to do 1 job; how much time would he take to do 1-(1/6) of the job?
R: 5/6 * 30= 25 days

I thought that if together they worked for 2 days, 1/6 of the projected was completed, so be would have to do 5/6 of the project?

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Dec 26, 2010 6:48 pm

sanju09 wrote:A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

A. 18 days
B. 27 days
C. 26.67 days
D. 16 days
E. 12 days

Plug in job = 60 units.
Rate for A alone = w/t = 60/20 = 3 units per day.
Rate for B alone = w/t = 60/30 = 2 units per day.
Since A quits 10 days before the project is completed, B works alone for 10 days.
Work completed by B alone in 10 days = r*t = 2*10 = 20 units.
Remaining work = 60-40 = 40 units.
These 40 units were completed by A+B working together (before A quit).
Combined rate for A+B working together = 3+2 = 5 units per day.
Time for A+B to complete 40 units = w/r = 40/5 = 8 days.

Total time = time for B alone + time for A+B together = 10+8 = 18 days.

The correct answer is A.

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eyelikecheese: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Sun Nov 14, 2010 8:46 am; GMAT Score:690

by eyelikecheese » Sun Dec 26, 2010 10:38 pm

Hey guys I'm arriving at a different answer. Can someone explain this to me.

1/20 +1/30 is 1/12 of the job/each day

So it takes 12 days to complete the job. Thus, 2 days into it, A quits.

1/6 of the job has been done in 2 days and B has 1/30 of the job for the remaining 5/6 of the job. This comes to 25 days+the original 2=27?

What am I computing wrong?

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun Dec 26, 2010 11:27 pm

eyelikecheese wrote:Hey guys I'm arriving at a different answer. Can someone explain this to me.

1/20 +1/30 is 1/12 of the job/each day

So it takes 12 days to complete the job. Thus, 2 days into it, A quits.

1/6 of the job has been done in 2 days and B has 1/30 of the job for the remaining 5/6 of the job. This comes to 25 days+the original 2=27?

What am I computing wrong?

You're assuming that A and B together has completed the job in 12 days and then you are saying A has left after 2 days! That makes your initial assumption (i.e. A and B together has completed the job in 12 days) baseless! And thus A did not left after 2 days.

After how many days A left the work depends upon the total number of days it took to complete the job. Thus it's a reverse calculation problem.

A left 10 days before the project is complete.
Thus for last 10 days only B has done the work => In last 10 days B has done (10/30) = 1/3 of the project.

Thus, A and B together has done 2/3 of the project.
To do 2/3 of the project A and B together took 12*(2/3) = 8 days

Thus the number of days the project took to be completed = Number of days together A and B worked + number of days only B worked = 8 + 10 = 18

The correct answer is A.

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Mon Dec 27, 2010 5:32 pm

GMATGuruNY wrote:
sanju09 wrote:A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

A. 18 days
B. 27 days
C. 26.67 days
D. 16 days
E. 12 days
Plug in job = 60 units.
Rate for A alone = w/t = 60/20 = 3 units per day.
Rate for B alone = w/t = 60/30 = 2 units per day.
Combined rate for A+B together = 3+2 = 5 units per day.
Work completed by B alone in 10 days = r*t = 2*10 = 20 units.
Work to be completed by A+B = 60-20 = 40 units.
Time for A+B to complete 40 units = w/r = 40/5 = 8 days.
Total time = 10+8 = 18 days.

The correct answer is A.

i thought A and B work together in a couple of days then A quit and B continue working on the left job?

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Dec 27, 2010 8:08 pm

diebeatsthegmat wrote:i thought A and B work together in a couple of days then A quit and B continue working on the left job?

According to the question, A and B start working on the project together and A quits 10 days before the project is completed. Now mathematically the event is same as B worked alone for 10 days and then A joined with him! In both of the cases total number of days required will be same.

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Zerks87: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Sat Oct 16, 2010 8:15 am; Thanked: 9 times

by Zerks87 » Mon Jan 10, 2011 2:40 pm

Anurag@Gurome wrote:
diebeatsthegmat wrote:i thought A and B work together in a couple of days then A quit and B continue working on the left job?
According to the question, A and B start working on the project together and A quits 10 days before the project is completed. Now mathematically the event is same as B worked alone for 10 days and then A joined with him! In both of the cases total number of days required will be same.

Fantastic way of looking at the problem. Cuts out alot of calculations. Thank you

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