Q. 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 :
Answer: $latex 5\frac{5}{7}days&s=1$
Notes: (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.