Ferromagnetic ordering in a topological insulator can break time-reversal symmetry, realizing dissipationless electronic states in the absence of a magnetic field. The control of the magnetic state is of great importance for future device applications. We provide a detailed systematic study of the magnetic state in highly doped CrxSb2-xTe3 thin films using electrical transport, magneto-optic Kerr effect measurements and terahertz time domain spectroscopy, and also report an efficient electric gating of ferromagnetic order using the electrolyte ionic liquid [DEME][TFSI]. Upon increasing the Cr concentration from x = 0.15 to 0.76, the Curie temperature (Tc) was observed to increase by ~5 times to 176 K. In addition, it was possible to modify the magnetic moment by up to 50% with a gate bias variation of just ±3 V, which corresponds to an increase in carrier density by 50%. Further analysis on a sample with x = 0.76 exhibits a clear insulator-metal transition at Tc, indicating the consistency between the electrical and optical measurements. The direct correlation obtained between the carrier density and ferromagnetism - in both electrostatic and chemical doping - using optical and electrical means strongly suggests a carrier-mediated Ruderman-Kittel-Kasuya-Yoshida (RKKY) coupling scenario. Our low-voltage means of manipulating ferromagnetism, and consistency in optical and electrical measurements provides a way to realize exotic quantum states for spintronic and low energy magneto-electronic device applications.