Given that $a,b \in \{0,1,2,.........,9\}$ with $a+b \neq 0$ and that $\bigg(a, \large\frac{b}{10}$$\bigg)^x=\bigg(\large\frac{a}{10},\frac{b}{100}\bigg)^y$$-1000$ Then $\large\frac{1}{x}-\frac{1}{y}=$

Question

$$\begin {array} {1 1} (1)\;1 & \quad (2)\;\frac{1}{2} \\ (3)\;\frac{1}{3} & \quad (4)\;\frac{1}{4} \end {array}$$