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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
A can complete a project in 20 days and B can complete the same projec
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20 Sep 2021, 04:57
20 Sep 2021, 04:57
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Question Stats:
55% (02:10) correct
44% (02:40) wrong based on 18 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
(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days
Re: A can complete a project in 20 days and B can complete the same projec
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21 Sep 2021, 06:30
21 Sep 2021, 06:30
1
Let T be the total number of days to complete the project.
A can do \(\frac{1}{20}\) of work in one day and B can do \(\frac{1}{30}\) in one day and to gather they can for\( \frac{1}{20} + \frac{1}{30} = \frac{1}{12}\) of the work.
So if A quit 10 days before the project is over, then T-10 days both worked and 10 days B alone worked to complete 1 task.
\(1 = \frac{(T-10)}{12} + \frac{10}{30}\)
Solving to T, will be T = 18 days.
Answer is A) 18
A can do \(\frac{1}{20}\) of work in one day and B can do \(\frac{1}{30}\) in one day and to gather they can for\( \frac{1}{20} + \frac{1}{30} = \frac{1}{12}\) of the work.
So if A quit 10 days before the project is over, then T-10 days both worked and 10 days B alone worked to complete 1 task.
\(1 = \frac{(T-10)}{12} + \frac{10}{30}\)
Solving to T, will be T = 18 days.
Answer is A) 18
Re: A can complete a project in 20 days and B can complete the same projec
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23 Apr 2024, 12:06
23 Apr 2024, 12:06
1
A's rate = 1/20
B's rate = 1/30
A's time = x
B's time = x+10
Work done = 1
Multiply rate by time and add to get work:
x/20 + (x+10)/30 = (3x+2x+20)/60
5x+20 = 60
5x=40
x=8
A worked for 8 days, so B worked for the same 8 days, then for 10 more days and completed the project.
Total time = 18 days
B's rate = 1/30
A's time = x
B's time = x+10
Work done = 1
Multiply rate by time and add to get work:
x/20 + (x+10)/30 = (3x+2x+20)/60
5x+20 = 60
5x=40
x=8
A worked for 8 days, so B worked for the same 8 days, then for 10 more days and completed the project.
Total time = 18 days
