Aptitude Question ID: 106005
A and B can do a piece of work in 8 days, b and C can do it in 24 days, while C and A can do it in $latex 8\frac{4}{7}\ days&s=1$. In how many days can C do it alone ?
[A]10 days
[B]30 days
[C]40 days
[D]60 days
60 days
(A + B)’s 1 day’s work $latex = \frac{1}{8}&s=1$
(B + C)’s 1 day’s work $latex = \frac{1}{24}&s=1$
(C + A)’s 1 day’s work $latex = \frac{7}{60}&s=1$
On adding,
2(A + B + C)’s 1 day’s work $latex = \frac{1}{8}+\frac{1}{24}+\frac{7}{60} = \frac{15+5+14}{120} = \frac{34}{120}&s=1$
∴ (A + B + C)’s 1 day’s work $latex = \frac{17}{120}&s=1$
∴ C’s 1 day’s work $latex = \frac{17}{120}-\frac{1}{8} = \frac{17-15}{120} = \frac{1}{60}&s=1$
∴ C alone will complete the work in 60 days.
Hence option [D] is correct answer.