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?

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

@ INR

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

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