Abstract:- Suppose $X$ is a minimal surface, which is a ramified double covering $\pi:X\to S$, of a rational surface $S$, with dim $|-K_S|\geq 1$. And suppose $L$ is a divisor on $S$, such that $L^2\geq 7$ and $L\cdot C\geq 3$ for any curve $C$ on $S$. Then the divisor $K_X+\pi^*L$ on $X$, is base-point free and the multiplication map in it's section ring : $Sym^r(H^0(K_X+\pi^*L))\to H^0(r(K_X+\pi^*L))$, is surjective for all $r\geq 1$. In particular this implies, when $S$ is also smooth and $L$ is an ample line bundle on $S$, that $K_X+n\pi^*L$ embeds $X$ as a projectively normal variety for all $n\geq 3$. In this talk we will present this result and various things associated to it.