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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?

Options:
A .  18 days
B .  24 days
C .  30 days
D .  36 days
Answer: Option A

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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