The efficiency bit comes from the fact that it is more efficient to move a lot of air a little instead of a little air a lot. Therefore if the core exhaust is mixed with the bypass, the bypass exhaust speed is higher and the core ehaust speed lower. Since there is more bypass exhaust than core, more thrust is developed.
Talking about noise, when the core/bypass exhaust is mixed this produces a VERY turbulent flow. Instead of having two shear zones as in a un-mixed exhaust system, there is now only one in a mixed exhaust system. This can actually be louder, it is all in how the two are mixed....you may have seen the wavy exhaust cowls/guides on the newer turbo fans (Trent 700??). These induce a series of votices which help spead the shear zone out over a larger cross section. This increase in shear zone size is what will reduce the noice output.
Mr L.