Question : A alone can complete a work in 18 days and B alone in 15 days. B alone worked at it for 10 days and then left the work. In how many more days, will A alone complete the remaining work?
Option 1: $5$ days
Option 2: $5\frac{1}{2}$ days
Option 3: $6$ days
Option 4: $8$ days
Correct Answer: $6$ days
Solution :
Time taken by A to complete the work = 18 days
Time taken by B to complete the work = 15 days
Work done by A in a day = $\frac{1}{18}$
Work done by B in a day = $\frac{1}{15}$
Work done by B in 10 days = $\frac{10}{15}$
Work left = $1-\frac{10}{15}=\frac{1}{3}$
So, time taken by A to complete the remaining work = $\frac{\text{Work left}}{\text{work done in a day}} = \frac{\frac{1}3}{\frac{1}{18}}=6$
Hence, the correct answer is 6 days.
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