The elevated co-occurrence of arsenic and fluoride in surface and groundwater poses risks to human health in many parts of the world. In single and competitive batch equilibrium studies, this research focuses on As(V) and F adsorption by activated carbon. BET, XRD, FESEM, EDS, and FTIR analysis depicted the structural characteristics of activated carbon. The influence of dosage, pH, and contact time were investigated in single and simultaneous adsorption systems. The maximum adsorption capacity of activated carbon for arsenic and fluoride was 3.58 mg/g and 2.32 mg/g, respectively. Time-dependent studies indicated that pseudo-second-order kinetic models fit better than pseudo-first-order, Elovich, and intraparticle diffusion kinetic models. The non-linear regression analysis of Langmuir, Freundlich, Toth, Redlich Petersons, and Modified Langmuir Freundlich models was used to determine single-component sorption capabilities and parameters. Additionally, the simultaneous removal study was rigorously modeled and compared using the Extended Langmuir (EL), Extended Langmuir Freundlich (ELF), Modified Competitive Langmuir (MCL), and Jeppu Amrutha Manipal Multicomponent (JAMM) isotherm models, and competitive mechanisms were interpreted for simultaneous adsorption system. Further, the model performance was evaluated by statistical error analysis using the normalized average percentage error (NAPE), root mean square errors (RMSE), and the correlation coefficient (R2). According to the modeling results, single equilibrium data fitted better with the Modified Langmuir Freundlich isotherm model, with a higher R2 of 0.99 and lower NAPE values of 3.8% and 1.28% for As(V) and F, than other models. For the binary adsorption, the Extended Langmuir Freundlich isotherm model demonstrated excellent fit with low errors. All the competitive isotherm models fit the As(V) and F simultaneous sorption systems well. Furthermore, the research unveiled a nuanced hierarchy of isotherm fitting, with ELF > EL > MCL > JAMM in varying arsenic at a constant fluoride and ELF > JAMM > EL > MCL in varying fluoride at a constant arsenic. In addition, competitive studies divulged crucial insights into selectivity adsorption as As(V) exhibits a pronounced adsorption selectivity over F. In essence, As(V) showed more pronounced antagonistic behavior over F, whereas F exhibited a less significant change in the adsorption in the presence of arsenic.