**Solution**

: Let the numbers are $x$ and $y$.

$$

\begin{array}{c}

\therefore \quad x+y=11 \\

x y=18

\end{array}

$$

Dividing eqn. 1 by 2 ,

$$

\begin{aligned}

& \frac{x+y}{x y}=\frac{11}{18} \\

\therefore \quad & \frac{1}{y}+\frac{1}{x}=\frac{11}{18} ; \text { Ans. }

\end{aligned}

$$