I hope this can answer your question.
for example, A330 (Trent 700) is a mixed engine (hot and cold nozzles are merged inside the integrated exhaust nozzle) which has convergent jet nozzles and is used for examining the effect of the component performance ( efficiency for the compressors and turbines, pressure loss for the combustor) on the engine performance. once the fan pressure ratio is selected, the bypass ratio is determined for a given turbine inlet tempreture and overall pressure ratio.
With the mixed engines, the choice of fan pressure ratio fixes the pressure downstream of the LP turbine and hence the power output from the turbine. For a given choice of turbine entry temp. and overall pressure ratio, the fan pressure ratio therefore fixes the bypass ratio. ( this is in contrast with the unmixed engine eg."PW 4000" for which the bypass ratio and fan pressure ratio can be selected independently, at least over some range.)
The benefit conferred by the working line being further to the right for the mixed engine augments the small increase in thrust arising directly from the mixing of core and bypass flow. it means the pressure ratio falls more rapidly as turbine inlet tempreture decreases, but the mass flow thru the fan decreases proportionally less. this steeper working line of the fan is a primary reason for the use of the mixer ( sorry can't show graph here). This maximum fan pressure ratio occurs during climb, but of far greater concern to the overall fuel consumption are conditions when the engine is throttled back somewhat, such as cruise, because the engine operates for much longer at this condition. A further benefit is that there is a smaller drop in rotational speed required to reduce thethrust with the steeper working line; this higher rotational speed, relative to that for the unmixed engine, means that at the reduced thrust condition for cruise the LP turbine will operate at lower value of change in stagnation enthalpt/blade speed(square) which is likely to give a further increase in efficiency.