P alone can complete a work in 15 days and Q alone can complete the same work in 12 days. They start the work together but after 3 days P leaves the work. How much time will Q take to finish the remaining work?

6.6 days

efficiency ∝ $\frac{1}{time}$

                   P   :   Q

time            15  :  12

efficiency       4  :  5    ⇒ total = 9

Total work = LCM of 12, 15 = 60

Work done by P and Q together in 3 days = efficiency of P & Q x 3

                                                                  = 9 x 3 = 27

Work left = 60 - 27 = 33

Time taken by Q alone to complete the remaining work = $\frac{remaining\;work}{efficiency}$

                     = $\frac{33}{5}$ = 6.6 days