Work Time : Working in parallel

This aptitude practice question is a Work Time problem solving question. Concept tested: It is a word problem in rates. Computing time taken to complete a task when part of the work is done by two people working in parallel.

Question

A and B can do a piece of work in 21 and 24 days respectively. They started the work together and after some days A leaves the work and B completes the remaining work in 9 days. After how many days did A leave?

1. 5
2. 7
3. 8
4. 6

  Correct Answer      Choice (2). A left after 7 days.

Explanatory Answer

Working alone B takes 24 days to complete the work.
∴ B completes \\frac{1}{24})th of the work in a day.
In the last 9 days when B works alone after A has left, B completes \\frac{9}{24}) i.e., \\frac{3}{8}^{th}) of the work.
Hence, 1 - \\frac{3}{8}) = \\frac{5}{8}^{th}) of the work is completed by A and B together.

Let A and B work together for 'x' days before A leaves.
In these x days, A and B will complete x (\\frac{1}{21}) + \\frac{1}{24})) of the work
We know A and B have completed \\frac{5}{8})th of the work when they worked together.
∴ x (\\frac{1}{21}) + \\frac{1}{24})) = \\frac{5}{8})
x (\\frac{8 + 7}{168})) = \\frac{5}{8})
=> x (\\frac{15}{168})) = \\frac{5}{8})
x = 7 days.

  The correct answer is Choice (2).