GMAT Practice Questions | GMAT Rates Q8

A GMAT quant 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. A medium difficulty, GMAT 650 level, quantitative reasoning sample question.

Question 8: 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

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Video Explanation

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Explanatory Answer | GMAT Work Time

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.
The value of x is the answer to the question.

B worked 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
\\frac{3(x - 10) + 2x}{60}) = 1
3x - 30 + 2x = 60
5x = 90 or x = 18

Choice A is the correct answer.