In this paper, we discuss the evolution of the universe by considering Λ and G as time varying constants with different choices of Λ. We choose the polytropic equation of state as the total energy content and find approximate values of the constant parameters for the cold dark matter and radiation components of the fluid of the universe. We also mention different possibilities for the constant parameters in order to interpret quintessence, vacuum, and phantom dark energy phases of the universe. Also, we find the conditions on the different constant parameters under which the behavior of G and Λ is consistent with the present observations. Finally, we calculate the statefinder parameters in this scenario.