A is thrice as efficient as B, A takes 16 days less than B to complete a work. If they work together, in how many days, will the work be completed?

6 days

Time taken ∝ \(\frac{1}{efficiency}\)

                                  A  :  B

ratio of efficiency        3  :  1          

           time taken       1  :  3   ⇒ difference 2R = 16 

                                                                  R = 8

say, total work = 24

Efficiency of A & B together = 4

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

                                 = \(\frac{24}{4}\) = 6 days