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?

1. 18 days
2. 27 days
3. 26.67 days
4. 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).