A can do \(\frac{1}{3}\)rd of a work in 30 days, B can do \(\frac{2}{5}\)th of the same work in 24 days. They worked together for 20 days. C completes the remaining work in 8 days. Working together A, B and C will complete the same work in:

12

Time taken by A to  do whole work = 90 days

Time taken by B to do \(\frac{2}{5}\) part  of work is 24 days

Time taken by B to  do whole work = 60 days

A and B together work for 5 days .

Total work = Efficiency × Number of days

Total work = 5R × 20 = 100R

Remaining work = 180R - 100R = 80R

C completes the remaining work in 8 days

Efficiency of C = \(\frac{80R}{8}\) = 10R

Time taken by all of them together = \(\frac{180R}{15R}\)  =12 days