A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B a

Question

A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :

Options:

A . 4 days

B . 6 days

C . 8 days

D . 12 days

Answer: Option C

(A + B + C)'s 1 day's work = \(\frac{1}{6}\)

(A + B)'s 1 day's work = \(\frac{1}{8}\)

(B + C)'s 1 day's work = \(\frac{1}{12}\)

So , (A + C)'s 1 day's work = \(\left(2\times \frac{1}{6}\right)-\left(\frac{1}{8}+\frac{1}{12}\right)\)

= \(\left(\frac{1}{3}-\frac{5}{24}\right)\)

= \(\frac{3}{24}\)

= \(\frac{1}{8}\)

So, A and C together will do the work in 8 days.

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