# Work Time Practice: Word Problem

This quantitative aptitude practice question is a Work Time word problem. It is a moderate difficulty problem solving question. Concept tested: Time taken to complete a task when two people start working together and one of them leaves before the task is completed.

## 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

** Correct Answer** Choice (1). The project will be completed in 18 days.

## Explanatory Answer

If A can complete the project in 20 days, then A will complete \\frac{1}{20}^{th}) of the project in a day.

Similarly, 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.

Then, B would have worked for all x days.

A left 10 days before the project was completed. So, A did not work the last 10 days. So, A would have worked for (x - 10) days.

Therefore, A would have completed \\frac{x-10}{20})^{th} of the project and B would have complete \\frac{x}{30})^{th} of the project.

i.e., \\frac{x-10}{20}) + \\frac{x}{30}) = 1

\\frac{3(x - 10) + 2x}{60}) = 1

\\frac{5x - 30}{60}) = 1

5x - 30 = 60 or 5x = 90

Or x = 18

'x' is the total time taken to complete the project. So, the project was completed in 18 days.

The correct answer is Choice (1).

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- Number Theory
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