A college has a 7:8 boy-to-girl ratio. If boys increase by 20% and girls by 10%, what will the new ratio be?
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Answer: C. 21 : 22
Explanation
Multiplying the initial number of boys by 1.2 gives exactly 8.4 for the new total. Multiplying the initial number of girls by 1.1 yields exactly 8.8 for the new count. Simplifying the resulting decimal ratio of 8.4 to 8.8 produces the final fraction 21 to 22. Ratio quantities represent proportional relationships rather than absolute head counts within a given population group. Percentage increases are calculated by multiplying the original value by one plus the fractional growth rate. Ratios can be simplified by dividing both numerical terms by their greatest common divisor.
Option A suggests an incorrect simplification that fails to maintain proper proportional equivalence for the decimals. Option B represents an arithmetic mistake that incorrectly adds growth factors instead of multiplying them properly. Option D is incorrect because sufficient numerical data is provided in the prompt to solve the problem.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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