Comparative marksmanship with different firing rates: when B has missed 27 times, how many birds has A killed?

Introduction / Context:
This is a proportion and rate problem. Two shooters A and B fire in a fixed shot ratio and have different per-shot success rates. You must infer A’s kills when B’s number of misses is known.

Given Data / Assumptions:

• Shot ratio: A:B = 5:3.
• A kills once in 3 shots ⇒ success rate per shot = 1/3.
• B kills once in 2 shots ⇒ success rate per shot = 1/2 (miss = 1/2).
• B has missed 27 times.

Concept / Approach:
Interpret the “kills once in n shots” as a steady rate. For B, misses:kills ≈ 1:1 because success = 1/2. Use B’s misses to deduce B’s shots, then apply the shot ratio to find A’s shots and thereby A’s kills.

Step-by-Step Solution:

Verification / Alternative check:
Think in pairs of B’s shots: every 2 shots, B averages 1 kill and 1 miss. With 27 misses, there are 27 such pairs → 54 shots, aligning with the calculation.

Why Other Options Are Wrong:

• 60, 72, 90 birds: These assume incorrect conversions between misses, shots, and kills or ignore the 5:3 firing ratio.

Common Pitfalls:
Mixing up kills with misses for B, or applying the 5:3 ratio to kills instead of shots.

Final Answer:
30 birds