A rectangle's length and breadth increase by 10% and 25% respectively. What is the percentage area increase?
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Answer: B. 37.5%
Explanation
The net percentage increase for two successive percentage changes is calculated using the standard formula a plus b plus a b over one hundred. Substituting ten for the length increase and twenty-five for the breadth increase gives ten plus twenty-five plus ten times twenty-five over one hundred. Evaluating the expression gives thirty-five plus two point five, resulting in a total area increase of thirty-seven point five percent. Successive percentage changes do not simply add together linearly because the second percentage applies to the already modified value. The area of a rectangle equals length multiplied by breadth, making percentage changes multiplicative rather than additive. The net change formula accounts for the cross-product interaction between length and breadth modifications.
Option A underestimates the area increase by failing to account for the cross-product interaction term. Option C overshoots the correct net percentage calculation by misapplying the formula coefficients. Option D assumes a simple additive sum of thirty-five percent plus additional errors in the calculation.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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