Number of days A required do a piece of work : 16
Number of days B required do a piece of work : 12
Work done by A in one day: \(\frac{1}{16}\)
Work done by B in one day: \(\frac{1}{12}\)
A works alone for 2 days, so work completed by A in 2 days : \(2\times\frac{1}{16}=\frac{1}{8}\)
Work left = \(1-\frac{1}{8}=\frac{7}{8}\)
Work done by A and B together in one day: \(\frac{1}{16}+\frac{1}{12}=\frac{7}{48}\)
They can do the work together in \(\frac{48}{7}\) days.
But \(\frac{7}{8}\)th of the work is done by both A and B
∴ Time required to complete \(\frac{7}{8}\)th of the work together by A and B : \(\frac{7}{8}\times\frac{48}{7}\) = 6 days
∴ Time taken to finish the work 6 + 2 = 8 days ( here 2 is added because\(\frac{1}{8}\)work is done by A alone).
∴ Total time taken to finish the work: 8 days