# Rates Practice : Work Time Word Problem

This quant practice question is a Work Time problem solving question. Concept tested: It is a word problem in work and time. Solving the question entails knowing how to frame work time equations and solving them.

## Question

A, B and C can do a work in 5 days, 10 days and 15 days respectively. They started together to do the work but after 2 days A and B left. In how many days did C complete the remaining work?

1. 1 day
2. 3 days
3. 5 days
4. 4 days

Correct Answer      Choice (4). C completed the remaining task in 4 days.

If A, B and C work together for a day then they will finish ($$frac {1}{5}$ + $\frac{1}{10}$ + $\frac{1}{15}^{th}$) work = $\frac{11}{30}^{th}$ work. They work together for 2 days. Therefore in those two days they will finish 2 * $\frac{11}{30}$ = $\frac{11}{15}^{th}$ work. C completes the remaining$1 - $$frac{11}{15}$) = $\frac{4}{15}^{th}$ work. Working alone, C finishes $\frac{1}{15}^{th}$ work in one day. Therefore, C will finish $\frac{4}{15}^{th}$ work in 4 days. The correct answer is Choice$4).

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