# 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.

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).

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