A group of men can do a work in certain number of days. After having worked for 18 days, of them leave. To complete the remaining work, the remaining men take the same number of days as the initial number of men would have taken to complete the entire work. In how many days is the entire work done?
Question
A group of men can do a work in certain number of days. After having worked for 18 days, of them leave. To complete the remaining work, the remaining men take the same number of days as the initial number of men would have taken to complete the entire work. In how many days is the entire work done?
Solution
The problem is a bit tricky, but let's break it down:
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Let's denote the number of men as 'm' and the number of days they would take to complete the work as 'd'. So, the total work can be represented as 'm*d'.
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According to the problem, these men worked for 18 days and then 1/3 of them left. So, the work done in these 18 days is '2/3m * 18'.
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The remaining work is 'm*d - 2/3m * 18'.
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The problem states that the remaining men (which is 2/3m) take 'd' days to complete the remaining work. So, we can write this as '2/3m * d = m*d - 2/3m * 18'.
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If we solve this equation for 'd', we get 'd = 27'.
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So, the total time taken to complete the work is the time taken by the initial group of men (18 days) plus the time taken by the remaining men (27 days), which equals 45 days.
Therefore, the entire work is done in 45 days.
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