We define a new parameter $A_{k,n}$ involving Ramanujans theta-functions for any positive real numbers $k$ and $n$ which is analogous to the parameter $A_{k,n}$ defined by Nipen Saikia cite{NS1}. We establish some modular relation involving $A_{k,n}$ and $A_{k,n}$ to find some explicit values of $A_{k,n}$. We use these parameters to establish few general theorems for explicit evaluations of ratios of theta functions involving $varphi(q)$.