A alone can do \(\frac{2}{3}\) of a work in 20 days. B is 20% more efficient than A. C alone can do the same work in 5 days less than B. D is 20% less efficient than C. If they all work together, then the work will be completed in how many days ?

\(\frac{300}{49}\) days

Total time of A = 20 x  \(\frac{3}{2}\)= 30 days

According to question,

                        A           :          B

Efficiency           5          :           6

Time                 6          :            5

we know ,  6R = 30 days  So 5R = 25 days i.e. B takes 25 days

Time taken by C = 25 - 5 = 20 days

                      C          :          D

Efficiency         5          :          4

Time               4           :         5

As , 4R = 20 days

1R = 5 days  . So   5R = 25 days              

Total time taken by all of them together = \(\frac{300}{49}\) days