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# A can complete a project in 20 days and B can complete the

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Intern
Joined: 09 Sep 2012
Posts: 33
Location: United States
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Kudos [?]: 10 [2] , given: 33

A can complete a project in 20 days and B can complete the [#permalink]  21 Sep 2012, 04:16
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Difficulty:

65% (hard)

Question Stats:

55% (02:30) correct 45% (02:06) wrong based on 246 sessions
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
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 30392
Followers: 5094

Kudos [?]: 57432 [7] , given: 8811

Re: A can complete a project in 20 days and B can complete the [#permalink]  21 Sep 2012, 04:35
7
KUDOS
Expert's post
154238 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

The rate of A $$\frac{1}{20}$$ job per day;
The rate of B $$\frac{1}{30}$$ job per day.

Say they need $$t$$ days to complete the project.

According to the stem we have that B works for all $$t$$ days and A works only for $$t-10$$ days, thus $$\frac{1}{20}*(t-10)+\frac{1}{30}*t=1$$ --> $$t=18$$days.

Hope it's clear.
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Manager
Joined: 05 Jul 2012
Posts: 82
Location: India
Concentration: Finance, Strategy
GMAT Date: 09-30-2012
GPA: 3.08
WE: Engineering (Energy and Utilities)
Followers: 4

Kudos [?]: 31 [0], given: 8

Re: A can complete a project in 20 days and B can complete the [#permalink]  21 Sep 2012, 04:49
154238 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

Assume to total work to be 60 Units ( LCM of 20 & 30)
A does 3 units per day ( =60/20)
B does 2 units per day ( =60/30)
B works for 10 days alone work done = 2*10 = 20 units
A and B work together for the rest of the time
work left = 40 units
A and b together to 5 units oer day ( 2+3 = 5)
days required to do 40 units = 40/5 = 8

Total = 10+8 = 18
Intern
Joined: 09 Sep 2012
Posts: 33
Location: United States
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Kudos [?]: 10 [0], given: 33

Re: A can complete a project in 20 days and B can complete the [#permalink]  21 Sep 2012, 05:00
I am getting 27.. please tell me where i am going wrong.

The rate of A 1/20 job per day;
The rate of B 1/30 job per day:

If both are working together: 1/20 + 1/30 = 1/12, which means A and B working together will complete the project in 12 days.

if A left 10 days before the completion means they worked for 2 days together and B worked for 10 days more, so,
2*1/12 = 1/6 work done together => 5/6th project is remaining which wud be done by B,

B completes the project in.....30 days
B completes 5/6th project in......30*5/6=25

So, total of 25+2 = 27 days.

Please correct me if i am going in wrong direction.
Math Expert
Joined: 02 Sep 2009
Posts: 30392
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Kudos [?]: 57432 [4] , given: 8811

Re: A can complete a project in 20 days and B can complete the [#permalink]  21 Sep 2012, 05:13
4
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Expert's post
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BOOKMARKED
154238 wrote:
I am getting 27.. please tell me where i am going wrong.

The rate of A 1/20 job per day;
The rate of B 1/30 job per day:

If both are working together: 1/20 + 1/30 = 1/12, which means A and B working together will complete the project in 12 days.

if A left 10 days before the completion means they worked for 2 days together and B worked for 10 days more, so,
2*1/12 = 1/6 work done together => 5/6th project is remaining which wud be done by B,

B completes the project in.....30 days
B completes 5/6th project in......30*5/6=25

So, total of 25+2 = 27 days.

Please correct me if i am going in wrong direction.

Yes, working together they can complete the job in 12 days, but if A leaves at some point, then they no longer will need 12 days, they will need more. So, you cannot say that they worked together for 12-10=2 days.

Consider another approach:

In 10 days that B worked alone 10*1/30=1/3 of the job was done and 2/3 of the job was left to be done by A and B together.

Rate*Time=Job Done --> (1/20+1/30)*Time=2/3 --> Time=8. So, they worked together for 8 days, which means that total time is 10+8=18 days.

Hope it helps.
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Manager
Joined: 25 Jun 2012
Posts: 71
Location: India
WE: General Management (Energy and Utilities)
Followers: 3

Kudos [?]: 76 [0], given: 15

Re: A can complete a project in 20 days and B can complete the [#permalink]  21 Sep 2012, 09:26
A = w/20
B = w/30

A+B = w/20+w/30

Rate*Time = Work
(A+B)* (t-10) = W (A left the job 10 days before the total day)

solving we get t=28 days

putting total days = y-10= 28-10 = 18 days

I think I am wrong somewhere...
Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 18

Kudos [?]: 309 [0], given: 11

Re: A can complete a project in 20 days and B can complete the [#permalink]  14 Nov 2012, 06:08
d is the total days to complete the project.
A worked for d-10 days while b worked the whole d days.

Setup the Rate Equation like this $$(Rate of A) (d -10) + (Rate of B) (d) = 1$$

$$(\frac{1}{20}) (d-10) + (\frac{1}{30}) d = 1$$, 1 represents 100% of the project
$$3d -30 + 2d = 60 ==> 5d = 90 ==> d = 18 days$$

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Impossible is nothing to God.

Math Expert
Joined: 02 Sep 2009
Posts: 30392
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Kudos [?]: 57432 [0], given: 8811

Re: A can complete a project in 20 days and B can complete the [#permalink]  23 Jul 2013, 01:26
Expert's post
From 100 hardest questions.

Bumping for review and further discussion.
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Kudos [?]: 93 [0], given: 0

Re: A can complete a project in 20 days and B can complete the [#permalink]  10 Oct 2014, 20:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Manager
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Kudos [?]: 14 [0], given: 21

Re: A can complete a project in 20 days and B can complete the [#permalink]  11 Oct 2014, 11:12
I used logic and back solved to get this answer. We know the combined rate 12 days (1/30) + (1/20). So eliminate choice E as we know that A is stopping ten days earlier. Next look at 28 days and the 26.67 days. If we were to subtract 10 from each we would get something greater than 12 days, so we can eliminate those because if they worked together for more than 12 days the project would be complete. Next I looked at the 16 days subtracted out 10 days do this means they worked together for six days, completing half of the work (6 * (1/12)) and b would have 10 days (1/30) to complete the other half which is obviously not possible. Hence 18 is the answer
Re: A can complete a project in 20 days and B can complete the   [#permalink] 11 Oct 2014, 11:12
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