Work/Rate : GMAT Problem Solving (PS)
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# Work/Rate

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Intern
Joined: 16 Aug 2011
Posts: 10
Concentration: Finance, Entrepreneurship
GPA: 3.51
Followers: 0

Kudos [?]: 54 [0], given: 3

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15 Nov 2011, 23:54
00:00

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(N/A)

Question Stats:

43% (02:42) correct 57% (00:56) wrong based on 7 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

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

_________________

+1 Kudos is a great way of saying Thank you!! :D

Manager
Joined: 11 Sep 2009
Posts: 129
Followers: 5

Kudos [?]: 340 [0], given: 6

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16 Nov 2011, 01:16
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.
Intern
Joined: 16 Dec 2011
Posts: 49
GMAT Date: 04-23-2012
Followers: 0

Kudos [?]: 6 [0], given: 12

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30 Dec 2011, 03:04
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
Senior Manager
Joined: 13 May 2011
Posts: 317
WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
Followers: 21

Kudos [?]: 252 [0], given: 11

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30 Dec 2011, 10:56
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
Re: Work/Rate   [#permalink] 30 Dec 2011, 10:56
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