A and B can complete a piece of work in 30 days, B and C in 20 days while C and A in 15 days. If all of them work together, the time taken in completing the work will be :
[A]10\ days
[B]12\ days
[C]12\frac{2}{3}\ days
[D]13\frac{1}{3}\ days

\mathbf{13\frac{1}{3}\ days}
Work done by (A + B) in 1 day = \frac{1}{30}
Work done by (B + C) in 1 day = \frac{1}{20}
Work done by (C + A) in 1 day = \frac{1}{15}
On adding,
Work done by 2(A + B + C) in 1 day = \frac{1}{30}+\frac{1}{20}+\frac{1}{15} = \frac{3}{20}
∴ Work done by (A + B + C) in 1 day = \frac{3}{40}
∴ (A + B + C) will do the work in \frac{40}{3} = 13\frac{1}{3}\ days
Hence option [D] is correct answer.