Question : A and B can do a piece of work in 5 days and 10 days, respectively. They began the work together but A left after some days and B finished the remaining work in 8 days. After how many days did A leave?
Option 1: $3\frac{1}{8}$
Option 2: $5\frac{1}{8}$
Option 3: $6\frac{1}{8}$
Option 4: $\frac{2}{3}$
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Correct Answer: $\frac{2}{3}$
Solution :
Time taken by A alone to complete the work = 5 days
Work done by A alone in a day = $\frac{1}{5}$
Time taken by B alone to complete the work = 10 days
Work done by B alone in a day = $\frac{1}{10}$
Work done by B alone in 8 days = $\frac{8}{10}$
Work done by A and B together $= 1-\frac{8}{10}=\frac{2}{10}=\frac{1}{5}$
So they do $\frac{1}{5}$th part work in $\frac{\frac{1}{5}}{\frac{1}{5}+\frac{1}{10}}=\frac{1}{5}×\frac{10}{3}=\frac{2}{3}$ days
Hence, the correct answer is $\frac{2}{3}$.
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