Two quantities fall short of a third quantity by 30% and 37% respectively. By what percentage is the second quantity less than the first?
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Answer: C. 10%
Explanation
Letting the third reference quantity be one hundred, the first quantity is seventy and the second is sixty three. The difference between the first and second quantities is seven units based on the established baseline values. Dividing the difference of seven by the first quantity seventy yields a percentage shortfall of exactly ten percent. Percentage comparisons between two secondary quantities require using the correct baseline denominator as specified in the query. Base values in percentage problems provide the standard reference point against which relative increases or decreases are measured. Arithmetic reduction formulas calculate percentage differences by dividing absolute changes by the initial comparison value.
Fifteen percent overestimates the percentage shortfall through an incorrect choice of comparison denominator. Twelve percent is mathematically inconsistent with the exact ratio of seven to seventy derived from the values. Five percent underestimates the actual percentage difference calculated between the first and second quantities.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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