A towel, when bleached, loses 20% of its original length and 10% of its original breadth. What is the percentage decrease in the area of the towel after bleaching?

Introduction / Context:
This question tests the concept of percentage change in area when the dimensions of a rectangle change by certain percentages. A towel is treated as a rectangle whose length and breadth both shrink due to bleaching. Such problems are common in aptitude tests and help examine understanding of how percentage change in one dimension interacts multiplicatively with the percentage change in the other dimension to affect the total area.

Given Data / Assumptions:

• The original towel is rectangular with length L and breadth B.
• Length decreases by 20%, so the new length is 80% of L.
• Breadth decreases by 10%, so the new breadth is 90% of B.
• Area before bleaching is L * B, and area after bleaching is computed using the reduced dimensions.
• We are asked to find the percentage decrease in area, rounded in a standard way.

Concept / Approach:
Area of a rectangle is the product of its length and breadth. When each dimension is multiplied by a factor, the area is multiplied by the product of those factors. Here the effective area factor is 0.8 * 0.9. Once we find the new area ratio compared with the original, we can convert that change into a percentage decrease. This is a simple application of percentage and multiplication rules rather than direct subtraction of percentages.

Step-by-Step Solution:
Original area = L * B.New length = 80% of L = 0.8L, new breadth = 90% of B = 0.9B.New area = 0.8L * 0.9B = 0.72LB.So the new area is 72% of the original area.Percentage decrease in area = (1 − 0.72) * 100% = 28%.

Verification / Alternative check:
Take simple numbers to verify. Suppose L = 10 units and B = 10 units. Original area = 100 square units. After bleaching, new length = 8 units, new breadth = 9 units, new area = 72 square units. The decrease in area is 100 − 72 = 28 square units, which is a 28% decrease. This numerical example matches the algebraic calculation and confirms that the percentage decrease in area is correct.

Why Other Options Are Wrong:
Option 18% incorrectly treats the area change as an average rather than a product of two reductions. Option 32% overshoots the correct decrease and would correspond to a new area factor of 68%, which does not match 0.8 * 0.9. Option 20% corresponds to the length decrease alone and ignores the breadth decrease. Option 38% is even further away and does not arise from any reasonable combination of these percentage changes.

Common Pitfalls:
A common error is to simply add the percentage decreases (20% + 10% = 30%) and assume the area decreases by 30%, which is not correct because area depends on the product of dimensions, not their sum. Others may subtract one percentage from another or use approximate reasoning without computing the product of the factors. Forgetting that 80% and 90% translate to 0.8 and 0.9 in decimal form also leads to incorrect calculations.

Final Answer:
The percentage decrease in the area of the towel after bleaching is 28%.