For the solution of the full set of magnetohydrodynamic equations in the presence of gravity due to a central point-mass, a self-similar theory for a general polytrope has already suggested a set of exact time-dependent solutions by analytical methods for a gamma =4/3 polytrope, since gamma =4/3 is the simplest to treat. In the present paper while going for a complete set of self-similar solutions, the authors find that gamma =4/3 is the only physically-possible polytrope and that then, pressure is independent of the scalar function A and depends on angle and time only. They also obtain a specific form of time-dependence for the self-similar variable.