Percentage decrease in area after shrinkage in both dimensions: A towel loses 20% of its length and 10% of its breadth on bleaching. By what percentage does its area decrease?
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A18%
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B28%
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C38%
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D48%
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E30%
Answer
Correct Answer: 28%
Explanation
Introduction / Context:Area of a rectangle scales multiplicatively with changes in both dimensions. Here, each side shrinks by a different percentage, so combine the factors to find the net change in area.
Given Data / Assumptions:
- Length factor = 1 − 0.20 = 0.8.
- Breadth factor = 1 − 0.10 = 0.9.
Concept / Approach:New area factor = 0.8 * 0.9 = 0.72 → a 28% decrease relative to the original area (since 1 − 0.72 = 0.28 = 28%).
Step-by-Step Solution:
Original area A.New area = 0.8A * 0.9 = 0.72A.Percentage decrease = (A − 0.72A) / A * 100 = 28%.Verification / Alternative check:Try a numeric example: let original be 100 unit^2 → new 72 unit^2 → fall is 28 units → 28%.
Why Other Options Are Wrong:18%, 38%, 48%, 30% do not equal the product-based reduction combining −20% and −10% simultaneously.
Common Pitfalls:Adding percentage decreases (20 + 10 = 30) is incorrect because area is two-dimensional, requiring multiplicative combination of the factors.
Final Answer:28%