Problem Solving (PS) | Re: A contractor hires 100 men to finish a job in 50 days. After 14 days,

Total job =\(100m*50d = 5000md\) (\(md\) =man-days)

Job done in 14 days =\(100m*14d = 1400md\) . Remaining job =\(5000md - 1400md = 3600md\) .

Let the number of days that\((100-n)\) men worked be\(k\) , then\((100-n)*k + (100+n)*(50-14-k) = 3600\).

\(100k - nk + 3600 - 100k + 36n - nk = 3600\) .

\(36n - 2nk = 0\)
\(2nk = 36n\)
\(k = \frac{36}{2} = 18.\)
So, the\(2n\) men worked for\((36-18) = 18\) days.
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