A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
2(A + B + C)'s 1 day's work = \(\left(\frac{1}{30}+\frac{1}{24}+\frac{1}{20}\right) =\frac{15}{120}=\frac{1}{8}.\)
Therefore, (A + B + C)'s 1 day's work = \(\frac{1}{2\times8}=\frac{1}{16}\)
Work done by A, B, C in 10 days = \(\frac{10}{16}=\frac{5}{8}\)
Remaining work = \(\left(1-\frac{5}{8}\right)=\frac{3}{8}\)
A's 1 day's work = \(\left(\frac{1}{16}-\frac{1}{24}\right)=\frac{1}{48}\)
Now, \(\frac{1}{48}\) work is done by A in 1 day.
So, \(\frac{3}{8}\) work will be done by A in \(\left(48\times\frac{3}{8}\right)\) = 18 days.
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