Ionic liquids (ILs) have been emerged as the most promising class of electrolytes to achieve high energy density in electrochemical double layer capacitors (EDLCs) due to their unique properties. In this study, 1-butyl-4-methylpyridinium tetrafluoroborate ([BMPy][BF$_4$]) was explored as the electrolyte for graphene based EDLC in presence of co-solvent. Highly viscous [BMPy][BF$_4$] was diluted with two different organic solvents, namely acetonitrile (AN) andpropylene carbonate (PC). Different weight ratios of [BMPy][BF$_4$]: organic solvents were investigated and corresponding variation of EDLC’s performance was observed. Dynamic viscosity of these IL+solvent mixtures was also measured. Three electrochemical techniques, namely cyclic voltammetry, galvanometric charge discharge, electrochemical impedance spectroscopy were employed to analyse the effectiveness of these electrolyte–electrode systems. Maximum operating voltage 2.2 V was achieved for the four out of six studied systems. For PC based electrolytes, no effect of concentration of PC on operating potential window was observed. However with AN, electrochemical stability decreased with increase in solvent weight percentage. The highest specific energy (49 Wh kg$^{-1}$) and power (4.13 kW kg$^{-1}$) were obtained for 3:1 weight ratio of IL to AN. Reverse effect on specific capacitance and internal resistance was noticed for AN and PC based electrolytes.