A and B takes \(2\frac{2}{7}\) days and \(\frac{7}{25}\) 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?

\(\frac{4}{5}\)

In these type of questions:

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

Hence, Using direct formula, 

A + B will take = \(\sqrt {\frac{16}{7}\;×\;\frac{7}{25}}\)

                     = \(\frac{4}{5}\) days to complete the work