A can do 2/3rd of a work in 10 days while B can do 3/4th of the work in 15 days. Working together in how many days they will finish 3/5th of the work?

\(5\frac{1}{7}\) days

Time taken by A to do \(\frac{2}{3}\) part  of work is 10 days

Time taken by A to  do whole work = 15 days

Time taken by B to do \(\frac{3}{4}\) part  of work is 15 days

Time taken by B to  do whole work = 20 days  

\(\frac{3}{5}\) of work = \(\frac{3}{5}\) × 60R = 36R

Time taken by A & B together to do \(\frac{3}{5}\) of work   = \(\frac{36}{7}\) =  5\(\frac{1}{7}\) days