In aptitude (Ratio and Probability style word problems), A fires 5 shots for every 3 shots fired by B. A hits once in every 3 shots, while B hits once in every 2 shots. When B has missed 27 times, how many birds has A killed?

Introduction / Context:
This question blends ideas of ratios and success rates. Two shooters fire at birds with different accuracy and frequency. One shooter has a higher hit rate, but both follow fixed ratios of shots and outcomes. The question uses the number of misses for one shooter to determine how many hits the other shooter makes. This type of reasoning problem appears frequently in aptitude exams to test logical and quantitative skills together.

Given Data / Assumptions:

• A fires 5 shots for every 3 shots fired by B, so the ratio of shots A : B is 5 : 3.
• A hits once in every 3 shots, so A kills 1 bird per 3 shots.
• B hits once in every 2 shots, so B misses 1 shot for every 2 shots fired.
• B has missed 27 times in total.
• We must find how many birds A has killed, assuming the pattern remains consistent.

Concept / Approach:
For B, in every pair of 2 shots: 1 hit and 1 miss occur. So misses and hits for B are equal, and the number of misses tells us the number of such 2 shot cycles. If B has 27 misses, there must be 27 hits as well, and total shots for B are twice the number of cycles. Once we know B's shots, we use the 5 : 3 ratio to find A's number of shots, and then use A's accuracy (1 hit per 3 shots) to determine how many birds A kills.

Step-by-Step Solution:
Step 1: For B, each 2 shots contain 1 hit and 1 miss. Step 2: Therefore, the number of misses equals the number of hits for B. Step 3: Given B has missed 27 times, B has also hit 27 times. Step 4: Each pair of 2 shots produces 1 miss and 1 hit, so the number of pairs is 27. Step 5: Total shots fired by B = 2 * 27 = 54. Step 6: Using the ratio A : B = 5 : 3 for shots, if B fires 54 shots, the corresponding shots for A are: A's shots = 54 * (5 / 3) = 54 * 5 / 3 = 18 * 5 = 90. Step 7: A hits once in every 3 shots, so A's number of hits is 90 / 3 = 30. Step 8: Thus A has killed 30 birds.

Verification / Alternative check:
We can verify by summarizing the outcomes. B fired 54 shots and, by design, hit 27 birds and missed 27 birds. A fired 90 shots and hit 30 birds, missing 60. The ratio of shots A : B remains 90 : 54, which simplifies to 5 : 3, consistent with the given condition. The number of misses for B is exactly 27 as required, confirming that the calculations are correct.

Why Other Options Are Wrong:
60 birds, 72 birds, 90 birds, and 45 birds all correspond to different relationships between A's shots and B's misses and would break either the 5 : 3 shot ratio or A's success rate of 1 hit per 3 shots. Only 30 birds aligns with all constraints in the question.

Common Pitfalls:
A frequent mistake is to misinterpret the phrase hits once in every 2 shots for B and think this means 2 hits in 1 shot cycle. Others ignore the ratio of shots and try to work with absolute numbers prematurely. Always translate verbal conditions into simple ratios and success rates, and then link them step by step. Tracking shots, hits, and misses separately for each shooter avoids confusion.

Final Answer:
When B has missed 27 times, A has killed 30 birds.