tabsang wrote:

Jane and Ashley take 20 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it.

During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ?

(A) 10 Days

(B) 15 Days

(C) 16 Days

(D) 18 Days

(E) 20 Days

Assume Jane and Ashley worked together for x days without considering the 8 day leave of Jane. They would have completed

x(\frac{1}{40} + \frac{1}{20}) of the total work in those days. In the period when Jane took a 8 day leave, Ashley worked alone. So Ashley worked alone for 8 days. He would have completed

\frac{8}{40} th of the total work. The work finished before Jane started working alone, is

x(\frac{1}{20} + \frac{1}{40}) + \frac{8}{40}. This is equal to

\frac{4}{5} of the total work as in the period when Jane was working alone which is 4 days, she would have completed

\frac{4}{20} or

\frac{1}{5} of the work. Previously done work is therefore

\frac{4}{5}.

x(\frac{1}{40} +\frac{1}{20}) +\frac{8}{40} = \frac{4}{5}We have x = 8

Add to this the 8 days when Ashley worked alone and the 4 days when Jane worked alone. The total is 8+8+4=20 days.

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Srinivasan Vaidyaraman

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