A = 75 days ......... Rate (A) =\(\frac{ 1}{75}\)
B = 50 days ......... Rate (B) =\(\frac{ 1}{50}\)
C = 40 days ......... Rate (C) =\(\frac{ 1}{40}\)
Rate (A & B & C) = \(\frac{ 1}{75} + \frac{ 1}{50} + \frac{ 1}{40} = \frac{ 35}{600} = \frac{ 7}{120} \)
Rate (A & B) = \( \frac{ 1}{50} + \frac{ 1}{40} = \frac{ 5}{150} = \frac{ 1}{30} \)
Basic Formula : \(W = \frac{R}{T}\)
Let A,B,C together work for \( d\) days
Therefore \(W(A,B,C) = R(A,B,C) * d = \frac{7d}{120}\)
Work left = \(1 - \frac{7d}{120}\)
No. of days worked by only A&B =\( \frac{(work left) }{ Rate(A,B)}\) = \((1 - \frac{7d}{120})/ \frac{ 1}{30}\) = \(\frac{(120-7d)}{4}\)
Now given
\(d + \frac{(120-7d)}{4} = 18\)
\(=> d = 16\)
Hence, C left \(18-16 = 2 days\) before the work is completed
_________________
Shrekey
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