The ratio of efficiencies of A and B is 3 : 7, A takes 48 days more than B to complete a work. If they work together, in how many days, will the work be completed?

12 days

Time taken ∝ \(\frac{1}{efficiency}\)

                                  A  :  B

ratio of efficiency         3  :  7          

           time taken       7  :  3   ⇒ difference 4R = 48 

                                                                  R = 12

Total work = (3 + 7) 12 = 120

Efficiency of A & B together = 10

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

                                 = \(\frac{120}{10}\) = 12 days