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

Author Message
Intern
Joined: 16 Aug 2011
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Concentration: Finance, Entrepreneurship
GPA: 3.51
A can complete a project in 20 days and B can complete the same projec [#permalink]

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16 Nov 2011, 00:54
00:00

Difficulty:

55% (hard)

Question Stats:

44% (01:16) correct 56% (01:13) wrong based on 9 sessions

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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

OPNE DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/a-can-complet ... 39311.html

[Reveal] Spoiler:
This is my logic -
A's rate is 1/20 and B's rate is 1/30. Together they can complete the project in 12 days.
# of days the project has been completed is 'x'. Therefore, A and B work together for (x-10) days, and can complete (x-10)/12 of the project.
B alone has to complete x - (x-10)/12 of the project --> 12 x - x + 10 / 12 --> 11x + 10 / 12
So if B can complete the project in 30 days, then he can complete [(11x + 10)/12] of the project in [(11x + 10)/12]*30 days
Total time taken to complete the project would then be (x-10)/12 + (330x + 300)/12 = x
But that equation is obviously incorrect cause it gives a negative value. What have I missed?
[Reveal] Spoiler: OA

_________________

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Kudos [?]: 66 [0], given: 3

Manager
Joined: 11 Sep 2009
Posts: 129

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Re: A can complete a project in 20 days and B can complete the same projec [#permalink]

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16 Nov 2011, 02:16
Let X = the number of days taken to complete the project.

The amount of work done by A is (x-10) * (1/20).
The amount of work done by B is (x) * (1/30).

(1/20)*(x-10) + (1/30)*(x) = 1
(x/20) + (x/30) - (10/20) = 1
5x/60 = 3/2
x = 90/5
x = 18

Therefore, the answer is A: 18.

Kudos [?]: 431 [0], given: 6

Intern
Joined: 16 Dec 2011
Posts: 46

Kudos [?]: 7 [0], given: 12

GMAT Date: 04-23-2012
Re: A can complete a project in 20 days and B can complete the same projec [#permalink]

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30 Dec 2011, 04:04
two ways to solve it :-

first :-

use formula:-
t-10/20 + t/ 30 =1
we will get t = 18 days

second :-

in last 10 days b has done 1/3 rd of job alone
so A anb B together has done 2/3rdof job in first X Days , we have to find value of X ,
in sinlge day both togther will do 1/20th + 1/30th = 1/12th of job

means 1/12th job is done together by A and B in sinlge day
1/12 job ........................ in a day
full job in ...................... 12 days
2/3 rd of job ................ 12*2/3 days = 8 days

so all toghether they will take 10 + 8 = 18 days

Kudos [?]: 7 [0], given: 12

Senior Manager
Joined: 13 May 2011
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WE 1: IT 1 Yr
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Re: A can complete a project in 20 days and B can complete the same projec [#permalink]

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30 Dec 2011, 11:56
Rate together is= 1/20+1/30=1/12
Total T days needed. So, together they work (T-10) days.
therefore, 1/12*(T-10)+(1/30)*10=1 [work done together + work done by B= whole work]
solving for T = 18

Kudos [?]: 292 [0], given: 11

Math Expert
Joined: 02 Sep 2009
Posts: 42253

Kudos [?]: 132740 [0], given: 12360

Re: A can complete a project in 20 days and B can complete the same projec [#permalink]

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14 Aug 2017, 22:11
mk87 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

[Reveal] Spoiler:
This is my logic -
A's rate is 1/20 and B's rate is 1/30. Together they can complete the project in 12 days.
# of days the project has been completed is 'x'. Therefore, A and B work together for (x-10) days, and can complete (x-10)/12 of the project.
B alone has to complete x - (x-10)/12 of the project --> 12 x - x + 10 / 12 --> 11x + 10 / 12
So if B can complete the project in 30 days, then he can complete [(11x + 10)/12] of the project in [(11x + 10)/12]*30 days
Total time taken to complete the project would then be (x-10)/12 + (330x + 300)/12 = x
But that equation is obviously incorrect cause it gives a negative value. What have I missed?

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.

OPNE DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/a-can-complet ... 39311.html
_________________

Kudos [?]: 132740 [0], given: 12360

Re: A can complete a project in 20 days and B can complete the same projec   [#permalink] 14 Aug 2017, 22:11
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