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 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]$latex 10\ days$
[B]$latex 12\ days$
[C]$latex 12\frac{2}{3}\ days&s=1$
[D]$latex 13\frac{1}{3}\ days&s=1$
$latex \mathbf{13\frac{1}{3}\ days}&s=1$
Work done by (A + B) in 1 day $latex = \frac{1}{30}&s=1$
Work done by (B + C) in 1 day $latex = \frac{1}{20}&s=1$
Work done by (C + A) in 1 day $latex = \frac{1}{15}&s=1$
On adding,
Work done by 2(A + B + C) in 1 day $latex = \frac{1}{30}+\frac{1}{20}+\frac{1}{15} = \frac{3}{20}&s=1$
∴ Work done by (A + B + C) in 1 day $latex = \frac{3}{40}&s=1$
∴ (A + B + C) will do the work in $latex \frac{40}{3} = 13\frac{1}{3}\ days&s=1$
Hence option [D] is correct answer.