In this study, we have examined the behavior of two fluids within the framework of $f(T)$ gravity, while taking into account observational constraints. Our focus was specifically on the Locally Rotationally Symmetric Bianchi-I Universe in the context of $f(T)$ theory of gravity. By investigating the evolution of the universe, we utilized various cosmological parameters, such as the deceleration parameter, equation of state parameter, density parameter, pressureand statefinder diagnostics. Additionally, we analyzed the geometric properties of the model. In the teleparallel theories, we derived the torsion scalar T from the given metric's torsion tensor.