Step 1: Understand the carbon content for various steels and cast iron.
- Hypo-eutectoid steel has less than 0.8\% carbon (option I),
- Hyper-eutectoid steel has more than 0.8\% carbon but less than 2\% (option II),
- Hypo-eutectic cast iron has less than 2.0\% carbon (option III),
- Hyper-eutectic cast iron has more than 2.0\% carbon (option IV).
Step 2: Conclusion
The correct matching is:
- (A) Hypo-eutectoid steel → (I),
- (B) Hyper-eutectoid steel → (II),
- (C) Hypo-eutectic Cast Iron → (IV),
- (D) Hyper-eutectic Cast Iron → (III).
Final Answer:
\[
\boxed{(A) (I), (B) (II), (C) (IV), (D) (III)}
\]