If A and B together can complete a piece of work in 20 days, B and C in 10 days and C and A in 12 days, then A, B and C together can complete the same work in :
Q. If A and B together can complete a piece of work in 20 days, B and C in 10 days and C and A in 12 days, then A, B and C together can complete the same work in :
Answer: $latex 8\frac{4}{7}\ days&s=1$
Notes: (A + B)'s 1 day's work $latex = \frac{1}{20}&s=1$ (B + C)'s 1 day's work $latex = \frac{1}{10}&s=1$ (C + A)'s 1 day's work $latex = \frac{1}{12}&s=1$ On adding, 2(A + B + C)'s 1 day's work $latex = \frac{1}{20}+\frac{1}{10}+\frac{1}{12} = \frac{3+6+5}{60} = \frac{7}{30}&s=1$ ∴ (A + B + C)'s 1 day's work $latex = \frac{7}{60}&s=1$ ∴ Hence, the work will be completed in $latex \frac{60}{7} = 8\frac{4}{7}\ days&s=1$. Hence option [C] is correct answer.