# GMAT Quant Practice : Work Time

Concept: Word problem - convert words to equations.

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?

1. 18 days
2. 27 days
3. 26.67 days
4. 16 days
5. 12 days

Video explanation provided for this question

A 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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