A and B can do a piece of work in 12 days and 36 days, respectively. Both work for 4 days and then A leaves. How long (in days) will B take to complete the remaining work?
20
A's one-day work is \(\dfrac{1}{12}\) and B's one-day work is \(\dfrac{1}{36}\).
Their combined one-day work is \(\dfrac{1}{12} + \dfrac{1}{36} = \dfrac{3 + 1}{36} = \dfrac{4}{36} = \dfrac{1}{9}\).
In 4 days together they complete \(4 \times \dfrac{1}{9} = \dfrac{4}{9}\) of the work.
The remaining work is \(1 - \dfrac{4}{9} = \dfrac{5}{9}\).
B alone completes this in \(\dfrac{5}{9} \div \dfrac{1}{36} = \dfrac{5}{9} \times 36 = 20\) days.
Hence, B takes 20 days to complete the remaining work.
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