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
5. 4 days

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

Explanatory Answer

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).