Comparative marksmanship with different firing rates: when B has missed 27 times, how many birds has A killed?
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A30 birds
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B60 birds
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C72 birds
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D90 birds
Answer
Correct Answer: 30 birds
Explanation
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:
B’s miss probability per shot = 1/2, so expected misses equal expected kills.Given misses = 27, expected kills ≈ 27. Therefore, B’s shots ≈ 54.Shot ratio A:B = 5:3, hence A’s shots = (5/3) * 54 = 90.A’s kills = A’s shots * (1/3) = 90 * (1/3) = 30.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