Question : Three people A, B, and C worked together and finished a work in 9 days. If A alone can finish the same work in 18 days, and B alone in 30 days, then the number of days C alone will take is:
Option 1: 36 days
Option 2: 45 days
Option 3: 40 days
Option 4: 54 days
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Correct Answer: 45 days
Solution : Let $x$ be the total work. A alone can finish the same work in 18 days. So 1 day's work of A = $\frac{1}{18}$ of the work B alone can finish the same work in 30 days. So 1 day's work of B = $\frac{1}{30}$ of the work Let C take $y$ days to complete the work alone. When A, B, and C work together, their combined work rate is $\frac{1}{18}+\frac{1}{30}+\frac{1}{y}$ of the work per day. The combined work rate of A, B, and C is given by $\frac19$ of the work per day. ⇒ $\frac{1}{18}+\frac{1}{30}+\frac{1}{y}=\frac{1}{9}$ ⇒ $\frac{1}{y}=\frac{1}{9}-\frac{1}{18}-\frac{1}{30}$ ⇒ $\frac{1}{y}=\frac{10-5-3}{90}$ ⇒ $\frac{1}{y}=\frac{2}{90}=\frac{1}{45}$ ⇒ $y=45$ days Hence, the correct answer is 45 days.
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