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Work and Time - July 05, 2004

The GMAT Sample Math question for the day is from the topic Work and Time.

Question
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 correct choice is (A) and the correct answer is 18 days.

Explanatory Answer
If A can do complete a project in 20 days, then A will complete th of the project in a day.
Similarly, B will complete th of the project in a day.
Let the total number of days taken to complete the project be x days.
Then, B would have worked for all x days, while A would have worked for (x – 10) days.

Therefore, A would have completed th of the project and B would have complete th of the project.
i.e.,
Solving for x, we get x = 18.
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