If A and B together can complete a piece of work in 20 days, B and C in 10 days and C and A in 12 days, then A, B and C together can complete the same work in :
[A]4\frac{2}{7}\ days
[B]\frac{7}{60}\ days
[C]8\frac{4}{7}\ days
[D]30\ days

\mathbf{8\frac{4}{7}\ days}
(A + B)’s 1 day’s work = \frac{1}{20}
(B + C)’s 1 day’s work = \frac{1}{10}
(C + A)’s 1 day’s work = \frac{1}{12}
On adding,
2(A + B + C)’s 1 day’s work = \frac{1}{20}+\frac{1}{10}+\frac{1}{12} = \frac{3+6+5}{60} = \frac{7}{30}
∴ (A + B + C)’s 1 day’s work = \frac{7}{60}
∴ Hence, the work will be completed in \frac{60}{7} = 8\frac{4}{7}\ days.
Hence option [C] is correct answer.