A GMAT Math practice question in rates. A word problem in work time. Your ability to convert information given in words to mathematical expressions and equations is the gist of what is tested in any GMAT word problem.

#### 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?

- 18 days
- 27 days
- 26.67 days
- 16 days
- 12 days

#### Explanatory Answer

Video explanation provided for this questionA can complete a project in 20 days. So, A will complete \\frac{1}{20}\\)^{th} of the project in a day.

B can complete a project in 30 days. So, B will complete \\frac{1}{30}\\)^{th} of the project in a day.

Let the total number of days taken to complete the project be x days.

B worked for all x days. However, A worked for (x - 10) days because A quits 10 days before the project is completed.

In a day, A completes \\frac{1}{20}\\)^{th} of the project.

Therefore, A would have completed \\frac{x - 10}{20}\\)^{th} of the project in (x - 10) days.

In a day, B completes\\frac{1}{30}\\)^{th} of the project.

Therefore, B would have completed \\frac{x}{30}\\)^{th} of the project in x days.

∴ \\frac{x - 10}{20} + \frac{x}{30}\\) = 1

Or x = 18.

Choice A is the correct answer.

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