A is twice as efficient as B, A takes 30 days less than B to complete a work. If they work together, in how many days, will the work be completed?

20 days

Time taken ∝ \(\frac{1}{efficiency}\)

                                  A  :  B

ratio of efficiency         2  :  1          

           time taken       1  :  2   ⇒ difference R = 30

say, total work = 60

Efficiency of A & B together = 3

Time taken by A and B = \(\frac{Total\; work}{Efficiency}\)

                                 = \(\frac{60}{3}\) = 20 days