Q. A and B together can do a work in 8 days, B and C together in 6 days, while C and A together in 10 days, if they all work together, then the work will be completed in :
Answer: $latex 5\tfrac{5}{47}days&s=1$
Notes: (A + B)'s 1 day's work $latex = \frac{1}{8}&s=1$.......(i)
(B + C)'s 1 day's work $latex = \frac{1}{6}&s=1$.......(ii)
(C + A)'s 1 day's work $latex = \frac{1}{10}&s=1$.......(iii)
On adding all above equations,
2(A + B + C)'s 1 day's work $latex = \frac{1}{8}+\frac{1}{6}+\frac{1}{10}&s=1$
$latex => \frac{15+20+12}{120} = \frac{47}{120}&s=1$
∴ (A + B + C)'s 1 day's work $latex = \frac{47}{240}&s=1$
∴ A, B and C together will finish the work in $latex \frac{240}{47} = 5\tfrac{5}{47}days&s=1$
Hence option [C] is correct answer
