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]

[B]

[C]

[D]

Work done by (A + B) in 1 day

Work done by (B + C) in 1 day

Work done by (C + A) in 1 day

On adding,

Work done by 2(A + B + C) in 1 day

∴ Work done by (A + B + C) in 1 day

∴ (A + B + C) will do the work in

Hence option [D] is correct answer.