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 $= \frac{1}{12}$
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 $\frac{60}{7} = 8\frac{4}{7}\ days$.