Step 1: Understanding the Concept:
Set up a ratio based on the number of shots, hits (kills), and misses for both individuals.
Step 2: Identifying the Vector of Change:
- B's hit rate: 1 kill in 2 shots (Meaning 1 miss in 2 shots).
- If B missed 27 times, B must have fired $27 \times 2 = 54 \text{ shots}$.
Step 3: Calculation:
- Ratio of A's shots to B's shots = $5 : 3$.
- If B fired 54 shots, A fired: $(5/3) \times 54 = 5 \times 18 = 90 \text{ shots}$.
- A's hit rate: 1 kill in 3 shots.
- A's total kills = $90 / 3 = 30 \text{ kills}$.
Step 4: Final Answer:
A has killed 30 times. Thus, the correct option is (b).