Question

A fibres 5 shots to B’s 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed

• A. 30 birds
• B. 60 birds
• C. 72 birds
• D. 90 birds

Answer 1

The Correct Option is A

To solve this problem, let's first analyze the given information and calculate the number of birds A kills.

1. A shoots 5 times for every 3 shots B takes.

2. A kills once in 3 shots; thus, A's killing probability is \(\frac{1}{3}\).

3. B kills once in 2 shots; thus, B's killing probability is \(\frac{1}{2}\).

4. B has missed 27 times, denoting B has shot a total number of times as \(27 + x\), where \(x\) is the number of successful kills B has made.

5. Since B kills once in 2 shots, the formula for B's total shots is \((\text{successful kills}) / (\text{kill probability}) = B's\text{ total shots}\), leading to \(x = (27 + x)/2\).

Simplifying yields:	\(2x = 27 + x\)	\(\Rightarrow x = 27\)
Therefore, B shot	\(27 + 27 = 54\) times.

6. During this period, A shoots proportionally based on their shooting rates, meaning A shoots \((5/3) \times 54 = 90\) times.

7. Since A kills once in 3 shots, the total number of birds A kills is \(90 / 3 = 30\) birds.

Therefore, the correct answer is 30 birds.