A and B can do a work in 12 days, B and C can do the same work in 15 days, C and A can do the same time work in 20 days. The time taken by A, B and C to do the same work is
A+B will do $$\frac{1}{12}$$ amount of work in a day.
B+C will do $$\frac{1}{15}$$ amount of work.
C+A will do $$\frac{1}{20}$$ amount of work.
Adding above 3 equation 2(A+B+C) = $$\frac{1}{5}$$
                 or (A+B+C) = $$\frac{1}{10}$$
Hence together A,B and C will do complete work in 10 days.
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