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 :

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 :
[A]4\tfrac{4}{9}days
[B]3\tfrac{3}{4}days
[C]5\tfrac{5}{47}days
[D]3\tfrac{3}{7}days

5\tfrac{5}{47}days
(A + B)’s 1 day’s work = \frac{1}{8}…….(i)
(B + C)’s 1 day’s work = \frac{1}{6}…….(ii)
(C + A)’s 1 day’s work = \frac{1}{10}…….(iii)
On adding all above equations,
2(A + B + C)’s 1 day’s work = \frac{1}{8}+\frac{1}{6}+\frac{1}{10}
=> \frac{15+20+12}{120} = \frac{47}{120}
∴ (A + B + C)’s 1 day’s work = \frac{47}{240}
∴ A, B and C together will finish the work in \frac{240}{47} = 5\tfrac{5}{47}days
Hence option [C] is correct answer.

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