A and B together can complete a work in 8 days and B and C together in 12 days. All of the three together can complete the work in 6days. In how much time will A and C together complete the work?

8
Let A and C complete the work in x days
(A+B)’s one day’s work= $latex \frac{1}{8}&s=1$
(B+C)’s one day’s work= $latex \frac{1}{12}&s=1$
(C+A)’s one day’s work= $latex \frac{1}{x}&s=1$
Then (A+B+B+C+C+A)’s one day’s work = $latex \frac{1}{8}+\frac{1}{12}+\frac{1}{x}&s=1$
2(A+B+C)’s one day’s work = $latex \frac{3x+2x+24}{24x}&s=1$
(A+B+C)’s 1 day’s work = $latex \frac{5x+24}{24x\times 2}&s=1$
According to the question (A+B+C)’s 1 day’s work = $latex \frac{1}{6}&s=1$
$latex =>\frac{1}{6} = \frac{5x+24}{24x\times 2}&s=1$
$latex => 30x + 144 = 48x$
∴ x = $latex \frac{144}{18}&s=1$ = 8 days
∴ option [B] is the right answer.