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?

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:

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%