A and B can do a piece of work in = 12 days
Work done by A and B in 1 day \(=\frac{1}{12}\)
B and C can do a piece of work in = 15 days
Work done by C and B in 1 day \(=\frac{1}{15}\)
A and c can do a piece of work in = 20 days
Work done by A and C in 1 day \(=\frac{1}{20}\)
Now adding, we get,
2(A+B+C) ’s 1 day work \(=\frac{1}{12}+\frac{1}{15}+\frac{1}{20}=\frac{5+4+3}{60}=\frac{12}{60}=\frac{1}{5}\)
A+B+C one day work \(=\frac{1}{5\times2}=\frac{1}{10}\)
∵ A’s 1 day work = (A+B+C)’s 1 day work – ( B+C)’s 1 day work
\(=\frac{1}{16}-\frac{1}{15}=\frac{3-2}{30}=\frac{1}{30}\)
∴ A can finish the work in \(=\frac{1}{\frac{1}{30}}\) = 30 days
