Question : A, B, and C together can do a piece of work in 6 days. A and B together can do the same work in 12 days. B alone can do the same work in 18 days. In how many days can A and C together do the same work?
Option 1: 9 days
Option 2: 10.5 days
Option 3: 8 days
Option 4: 7.5 days
Correct Answer: 9 days
Solution :
According to the question
(A + B + C)'s 1 day work = $\frac{1}{6}$
(A + B)'s 1 day work = $\frac{1}{12}$
B's 1 day work = $\frac{1}{18}$
⇒ (A + C)'s 1 day work = $\frac{1}{6} - \frac{1}{18}$ = $\frac{1}{9}$
⇒ Time taken by A and C together = $\frac{1}{Rate}$ = $\frac{1}{\frac{1}{9}}$ = 9 days
Hence, the correct answer is 9 days.
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