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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Question : A and B can finish a work together in 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days can A alone finish the job?
Option 1: 50 days
Option 2: 60 days
Option 3: 48 days
Question : A can finish a work in 15 days, B can finish the same work in 25 days. They work together for 5 days. The rest of the work is finished by A and C in 4 days. Then C alone can finish the work in:
Option 1: 18 days
Option 2: 24 days
Option 3: 20 days
Option 4: 21 days
Question : A, B, and C together can finish a piece of work in 20 days. A alone can finish the work in 40 days. What part of the work B and C together can finish in a day?
Option 1: $\frac{1}{5}$
Option 2: $\frac{1}{20}$
Option 3: $\frac{1}{10}$
Option 4: $\frac{1}{40}$
Question : Ram can complete a piece of work in 18 days, Reena can complete the same work in 12 days, and with the help of Shyam, they finish the same work in 6 days. In how many days can Shyam alone complete the same work?
Option 1: 42 days
Option 2: 36 days
Option 3: 30 days
Option 4: 24 days
Question : A alone can make a table in 30 days while B alone can make it in 15 days. B started work alone and worked for 8 days. In how many days A alone can finish the remaining work?
Option 1: 14 days
Option 2: 10 days
Option 3: 12 days
Option 4: 15 days
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