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# Twelve men can complete a work in 8 days. Three days after they start

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Re: Twelve men can complete a work in 8 days. Three days after they start [#permalink]
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Bunuel wrote:
Twelve men can complete a work in 8 days. Three days after they started the work, 3 more men joined. In how many days will all of them together complete the remaining work?

(A) 2
(B) 4
(C) 5
(D) 6
(E) 7

Solution:

We see that the rate of each man per day is (1/8)/12 = 1/96. For the first three days, then, the crew of twelve men have accomplished 12 x 3 x 1/96 of the job. Now, let’s let d be the number of days to complete the remaining work after 3 more men have joined. The work accomplished by the crew of 15 men is 15 x d x 1/96. Since the total job is equal to 1, we can create the equation:

1/96 x 12 x 3 + 1/96 x 15 x d = 1

3/8 + 5d/32 = 1

5d/32 = 5/8

d/32 = 1/8

d = 4