A towel, when bleached, is found to have lost 20% of its length and 10% of its breadth. What is the percentage decrease in its area?

Introduction / Context:
This question is a good example of percentage change applied to two dimensions of a rectangle. The towel is treated as a rectangle with length and breadth. When each dimension changes by a certain percentage, the area changes by a combined effect, which is not simply the arithmetic sum of the two percentages. Such problems appear in aptitude exams to test understanding of compound percentage and area relationships.

Given Data / Assumptions:
• Original length of the towel is L.• Original breadth of the towel is B.• Length decreases by 20%, so new length is 80% of L.• Breadth decreases by 10%, so new breadth is 90% of B.• We seek percentage decrease in area.

Concept / Approach:
The original area A1 of the towel is L * B. After bleaching, the new length is 0.8L and the new breadth is 0.9B. The new area A2 is therefore 0.8L * 0.9B = 0.72L * B. This means the new area is 72% of the original area. The percentage decrease is then 100% − 72% = 28%. This demonstrates how combined percentage effects on dimensions multiply rather than simply add.

Step-by-Step Solution:
Step 1: Let original area A1 = L * B.Step 2: Compute new length.Length decreases by 20%, so new length = 0.8L.Step 3: Compute new breadth.Breadth decreases by 10%, so new breadth = 0.9B.Step 4: Compute new area A2.A2 = 0.8L * 0.9B = 0.72L * B.Step 5: Express A2 as a percentage of A1.A2 / A1 = (0.72L * B) / (L * B) = 0.72.So new area is 72% of the original area.Step 6: Compute percentage decrease.Decrease = 100% − 72% = 28%.

Verification / Alternative check:
We can also think in terms of a percentage formula: the approximate net percentage change when two changes x% and y% affect area is x + y + (x * y) / 100, where decreases are taken as negative. Here, x = −20 and y = −10. So net change ≈ −20 + (−10) + (−20 * −10) / 100 = −30 + 2 = −28%. This confirms that the area decreases by 28% overall, matching the previous calculation.

Why Other Options Are Wrong:
Option A: 10% treats only one dimension or incorrectly averages the effect.Option B: 10.08% comes from misapplying percentage formulas or calculation errors.Option C: 20% simply adds one of the decreases and ignores the other dimension.

Common Pitfalls:
A common mistake is to add 20% and 10% and conclude that the area decreases by 30%, which is incorrect because changes in area are multiplicative. Another error is to apply the percentage decrease directly to area without considering that both dimensions are changed. Using either the product of factors (0.8 and 0.9) or the net percentage change formula helps avoid these misunderstandings.

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