Concurrent adsorptive removal of methylene blue (MB) and rhodamine B (RhB) onto durian rind (DR) agricultural waste, from an aqueous binary solution as a model of wastewater containing multiple synthetic dyes, was investigated. The concurrent adsorption of the dyes followed pseudo-second-order kinetics. The adsorption isotherm was well simulated by the Langmuir model, implying a monolayer adsorption to the surface with a homogeneous binding energy. The adsorption process was governed by external mass transfer through two-step intraparticle diffusion of the dyes onto the adsorbent surface. The adsorption efficiency of MB (96.4%) is much higher than that of RhB (56.3%). This is attributed to the higher rate constant for the adsorption of MB (0.348 g mg−1 min−1) as compared to that of RhB (0.151 g mg−1 min−1). The adsorption behavior suggested that the two cationic dyes in the binary solution diffused and adsorbed independently and randomly onto the DR surface. The adsorption capacity of MB and RhB in the binary solution (47.4 mg g−1 and 32.9 mg g−1, respectively) is lower than those of their single solute solutions (93.3 mg g−1 and 62.8 mg g−1, respectively), suggesting a competitive effect in their concurrent adsorption. This was confirmed based on the adsorption characteristics of the binary solution with different molar ratios. The competitive effect was attributed to either non-interactive or repulsive electrostatic interactions between the positively charged dyes in the binary system. The domination of MB is attributed to its smaller molecular size, higher planarity, and faster adsorption kinetics compared with RhB.