Step 1: Identify \(X\) and \(Y\) from the first reaction.
Potassium superoxide reacts with water as
\[
2KO_2+2H_2O
\rightarrow
2KOH+H_2O_2+O_2.
\]
Therefore,
\[
X=H_2O_2
\]
and
\[
Y=O_2.
\]
Step 2: Use \(X\) in the second reaction.
In alkaline medium, hydrogen peroxide reduces permanganate to manganese dioxide.
\[
2KMnO_4+3H_2O_2
\rightarrow
2MnO_2+3O_2+2KOH+2H_2O.
\]
Hence,
\[
Y=O_2
\]
and
\[
Z=MnO_2.
\]
Final Answer:
\[
\boxed{Y=O_2,\qquad Z=MnO_2}
\]
\[
\boxed{\text{Answer = (B)}}
\]