A, B, and C can complete a work in 10, 12, and 15 days, respectively. A and B work together for 3 days, after which A withdraws. B and C then work together. Find the number of days required by B and C to complete the remaining work.
3 days
A's one day work is \(\frac{1}{10}\), B's one day work is \(\frac{1}{12}\), and C's one day work is \(\frac{1}{15}\).
A and B together work for 3 days, so work done \(= 3\left(\frac{1}{10} + \frac{1}{12}\right) = 3 \times \frac{11}{60} = \frac{33}{60} = \frac{11}{20}\).
Remaining work \(= 1 - \frac{11}{20} = \frac{9}{20}\).
B and C together have a combined one day rate of \(\frac{1}{12} + \frac{1}{15} = \frac{5}{60} + \frac{4}{60} = \frac{9}{60} = \frac{3}{20}\).
Days required \(= \frac{9/20}{3/20} = 3\) days.
Hence, B and C together take 3 days to complete the remaining work.
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