AAPL wrote:GMAT Paper Tests
\(A\) 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
Let the 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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