A can do a piece of work in 20 days and B in 30 days. They work together for 5 days. How much work is left?
\(\frac{7}{12}\)
The rate of work is the fraction of the job completed in one day, found as the reciprocal of the number of days each person needs alone.
A's one-day work \(= \frac{1}{20}\) and B's one-day work \(= \frac{1}{30}\).
Working together, their one-day work \(= \frac{1}{20} + \frac{1}{30} = \frac{3+2}{60} = \frac{5}{60} = \frac{1}{12}\).
In 5 days they complete \(5 \times \frac{1}{12} = \frac{5}{12}\) of the whole work.
Work left \(= 1 - \frac{5}{12} = \frac{12-5}{12} = \frac{7}{12}\).
Key concept: combined rates of workers add up, and remaining work equals the whole (taken as 1) minus the work already done.
Hence the fraction of work still left is 7/12.
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