A and B takes \(5\frac{1}{3}\) days and \(8\frac{1}{3}\) days more for doing a piece of work respectively than the time taken by A and B together. In how many days will they finish the work together?

\(6\frac{2}{3}\)

In these type of questions:

Use direct formula : (A + B)'s time = \(\sqrt {More\;time\;taken\;by\;A\;×\;More\;time\;taken\;by\;B}\)

Here,

\(5\frac{1}{3}\) = \(\frac{16}{3}\)

\(8\frac{1}{3}\) = \(\frac{25}{3}\)

ATQ,

A + B will take = \(\sqrt {\frac{16}{3}\;×\;\frac{25}{3}}\)

                     =  \(\frac{20}{3}\)

                     = \(6\frac{2}{3}\)