A and B can do a piece of work in 12 days and 12 days, respectively. Both work for 3 days and then A leaves. How long (in days) will B take to complete the remaining work?
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A and B both work at rate \(\tfrac{1}{12}\) per day each, giving a combined rate of \(\tfrac{2}{12}=\tfrac16\) per day.
Work done together in 3 days: \(3\times\tfrac16 = \tfrac12\).
Remaining work: \(1-\tfrac12=\tfrac12\).
Time for B alone to finish: \(\dfrac{1/2}{1/12} = 6\) days.
Hence, B will take 6 more days to complete the remaining work.
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