A and B takes \(2\frac{1}{4}\) days and \(6\frac{1}{4}\) 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?

\(3\frac{3}{4}\)

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 = \(\sqrt {\frac{9}{4}\;×\;\frac{25}{4}}\)

                     =  \(\frac{15}{4}\)

                     = \(3\frac{3}{4}\) days to complete the work