A and B takes 9 days and 16 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?

12

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 = \(\sqrt {9\;×\;16}\) 

                     =  3 x 4 = 12 days to complete the work