Solution
Using 5,5,1,2,7,8,6,4 digits
\[
\begin{aligned}
& \mathrm{x}=\underset{\substack{\text { Repeating } \\
\text { digit }}}{{ }^{9} \mathrm{C}_{1}} \times \underset{\text { Non repeating }}{{ }^{8} \mathrm{C}_{7}} \times\left(\frac{9!}{2!}\right) \\
& \mathrm{x}=9.8 \frac{9!}{2!}=36(9!)
\end{aligned}
\]
Using 1,1,7,7,4,2,5,6,9 digits
\[
\mathrm{y}=\underset{\substack{\text { repeating } \\ \text { digits }}}{{ }^{9} \mathrm{C}_{2}} \times{ }_{\substack{\text { Non-repeating } \\ \text { digits }}}^{{ }^{7} \mathrm{C}_{5}} \times \frac{9!}{2!2!}
\]
\[
\begin{aligned}
& y=\left(\frac{9.8}{2}\right)\left(\frac{7.6}{2}\right)\left(\frac{9!}{2!2!}\right)=9(7) 3.9! \\
& \frac{x}{y}=\frac{36(9!)}{9(7)(3) 9!} \Rightarrow \frac{x}{y}=\frac{4}{21} \Rightarrow 21 x=4 y \text { Answer }(3)
\end{aligned}
\]
.
