A and B can complete a piece of work in 8 days, B and C can do it in 12 days, C and A do it in 8 days. A, B and C together can complete it in :
[A]4 days
[B]5 days
[C]6 days
[D]7 days

6 days
(A + B)’s 1 day’s work = \frac{1}{8}
(B + C)’s 1 day’s work = \frac{1}{12}
(C + A)’s 1 day’s work = \frac{1}{8}
On adding,
2(A + B + C)’s 1 day’s work = \frac{1}{8}+\frac{1}{12}+\frac{1}{8} = \frac{3+2+3}{24} = \frac{1}{3}
∴ (A + B + C)’s 1 day’s work = \frac{1}{6}
So the work will be completed in 6 days.
Hence option [C] is correct answer.