A and B together can do a work in 10 days. B and C together can do the work in 6 days. A and C together can do the work in 12 days. Then A, B and C together can do the work in :
A and B together can do a work in 10 days. B and C together can do the work in 6 days. A and C together can do the work in 12 days. Then A, B and C together can do the work in :
[A]14 days
[B]28 days
[C]$latex 5\frac{5}{7}days&s=1$
[D]$latex 8\frac{2}{7}days&s=1$
$latex 5\frac{5}{7}days&s=1$
(A + B)’s 1 day’s work $latex =\frac{1}{10}&s=1$
(B + C)’s 1 day’s work $latex =\frac{1}{6}&s=1$
(C + A)’s 1 day’s work $latex =\frac{1}{12}&s=1$
On adding all above equations,
2 (A + B + C)’s 1 day’s work $latex =\frac{1}{10}+\frac{1}{6}+\frac{1}{12}= \frac{6+10+5}{60}&s=1$
$latex =\frac{21}{60}=\frac{7}{20}&s=1$
∴ (A + B + C)’s 1 day’s work $latex =\frac{7}{40}&s=1$
∴ All three together will complete the work in $latex \frac{40}{7} = 5\frac{5}{7}&s=1$
Hence option [C] is correct answer.