Question : A and B can do a job in 10 days and 5 days, respectively. They worked together for two days, after which B was replaced by C and the work was finished in the next three days. How long will C alone take to finish 60% of the job?
Option 1: 18 days
Option 2: 30 days
Option 3: 25 days
Option 4: 24 days
Correct Answer: 18 days
Solution : Time taken by A to complete the work = 10 days Part of work done by A in a day = $\frac{1}{10}$ Time taken by B to complete the work = 5 days Part of work done by B in a day = $\frac{1}{5}$ Part of work done by A and B in a day = $\frac{1}{10}+\frac{1}{5} = \frac{3}{10}$ Part of work done by A and B in 2 days = $\frac{6}{10}$ Remaining work = $\frac{10-6}{10} = \frac{4}{10} = \frac{2}{5}$ Let the time taken by C to complete the work be $x$ days. Part of work done by C in a day = $\frac{1}{x}$ Part of work done by A and C in a day = $\frac{1}{10}+\frac{1}{x}$ Part of work done by A and C in 3 days = $\frac{3}{10}+\frac{3}{x}$ $\frac{2}{5} = \frac{3}{10}+\frac{3}{x}$ $⇒\frac{3}{x} = \frac{2}{5} - \frac{3}{10} = \frac{4-3}{10} = \frac{1}{10}$ $\therefore x = 3 × 10 = 30$ days Time taken by C to complete 60% of work = 0.6 × 30 = 18 days Hence, the correct answer is 18 days.
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Question : A and B can do a job in 10 days and 5 days, respectively. They worked together for two days, after which B was replaced by C and the work was finished in the next three days. How long will C alone take to finish 40% of the job?
Option 2: 12 days
Option 3: 15 days
Option 4: 10 days
Question : A can complete one-third of a work in 10 days and B can do $\frac{3}{5}$ th of the same work in 24 days. They worked together for 10 days. The remaining work was completed by C alone in 15 days. In how many days can C alone do $\frac{2}{3}$rd of the same work?
Option 1: 27
Option 2: 24
Option 3: 30
Option 4: 32
Question : A, B and C together can complete a work in 20 days. A and B together can complete the same work in 30 days. Then, C alone can complete the same work in how many days?
Option 1: 10 days
Option 3: 45 days
Option 4: 60 days
Question : To do a certain work, B would take time thrice as long as A and C together and C twice as long as A and B together. The three men together complete the work in 10 days. The time taken by A to complete the work separately is:
Option 1: 22 days
Option 2: 24 days
Option 3: 30 days
Option 4: 20 days
Question : A and B can do a piece of work in 10 days. B and C can do it in 12 days. C and A in 15 days. In how many days will C finish it alone?
Option 1: 24 days
Option 3: 40 days
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