(a) 10 days
A’s one days’ work = \(\frac{1}{20}\)
B’s one days’ work = \(\frac{1}{12}\)
Work done by A in 4 days = \(\frac{4}{20}\) = \(\frac{1}{5}\)
Remaining work = 1 - \(\frac{1}{5}\) = \(\frac{4}{5}\)
(A + B)’s 1days’ work = \(\frac{1}{20}\) + \(\frac{1}{12}\) = \(\frac{2}{15}\)
\(\therefore\) Number of days to do the remaining work = \(\frac{4}{5}\div\frac{2}{15}\) = \(\frac{4}{5}\times\frac{15}{2}\) = 6 days
\(\therefore\) Total number of days taken in the completion of work = 6 + 4 = 10 days