A alone can do a work in 20 days, B alone in 30 days. They work together for 6 days, then A leaves. How many more days will B take to finish the remaining work?
15 days
Given: A completes the work in 20 days and B in 30 days; they work together 6 days, after which A leaves and B finishes the rest.
One day's work of A is \(\frac{1}{20}\) and of B is \(\frac{1}{30}\).
Together in one day they do \(\frac{1}{20} + \frac{1}{30} = \frac{3 + 2}{60} = \frac{5}{60} = \frac{1}{12}\).
In 6 days together they complete \(6 \times \frac{1}{12} = \frac{1}{2}\) of the work.
Remaining work is \(1 - \frac{1}{2} = \frac{1}{2}\).
B alone does \(\frac{1}{30}\) per day, so time to finish the rest is \(\frac{1/2}{1/30} = \frac{1}{2} \times 30 = 15\) days.
Thus B needs 15 more days after A leaves.
Hence the remaining work will take B 15 days.
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