A and B together can complete a piece of work in 18 days, B and C in 24 days and A and C in 36 days. In how many days, will all of them together complete the work?
[A]10 days
[B]12 days
[C]15 days
[D]16 days

16 days
(A + B)’s 1 day’s work = \frac{1}{18}
(B + C)’s 1 day’s work = \frac{1}{24}
(C + A)’s 1 day’s work = \frac{1}{36}
On adding,
2(A + B + C)’s 1 day’s work = \frac{1}{18}+\frac{1}{24}+\frac{1}{36} = \frac{4+3+2}{72} = \frac{1}{8}
∴ (A + B + C)’s 1 day’s work = \frac{1}{16}
∴ A, B and C together will complete the work in 16 days.
Hence option [D] is correct answer.