Question : A can do a piece of work in 10 days and B can do it in 12 days. They work together for 3 days. Then B leaves and A alone continues. 2 days after that C joins and the work is completed in 2 days more. In how many days can C do it, if he works alone?
Option 1: 30 days
Option 2: 50 days
Option 3: 40 days
Option 4: 60 days
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Correct Answer: 40 days
Solution :
A does work for 3 + 2 + 2 = 7 days
Work done by A = $\frac{7}{10}$
B does work for 3 days.
Work done by B = $\frac{3}{12}=\frac{1}{4}$
Total work completed by A and B
= $\frac{7}{10} + \frac{1}{4}$
= $ \frac{14}{20} + \frac{5}{20}$
= $ \frac{19}{20}$
So C does the remaining i.e. $1-\frac{19}{20}=\frac{1}{20}$ in 2 days.
$\therefore$ C alone will take 40 days to complete the task.
Hence, the correct answer is 40 days.
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