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

### Concept & Area Decrease Calculation When both dimensions of a rectangular object undergo a percentage decrease, the net percentage decrease in area is calculated using the net effect formula with negative values for decreases. $$ Net Change = x + y + \frac{x y}{100} $$ ### Step-by-Step Solution * Given that the length lost 20% and breadth lost 10%, we set $x = -20$ and $y = -10$. * Plug the values into the formula: $$ Net Change = -20 - 10 + \frac{(-20)(-10)}{100} $$ * Calculate the terms: $$ Net Change = -30 + \frac{200}{100} $$ * $$ Net Change = -30 + 2 = -28\% $$ * The negative sign indicates a decrease. ### Exam Strategy & Shortcut Use a base of 100 for the area by assuming sides of 10 and 10. New length = $10 - 2 = 8$. New breadth = $10 - 1 = 9$. New area = $8 \times 9 = 72$. The change from 100 to 72 is a drop of 28, representing a 28% decrease. ### Common Pitfall A common mistake is adding the two percentage losses together ($20\% + 10\% = 30\%$) without accounting for the fact that the reduction in breadth also applies to a now-shorter length. ### Final Answer Therefore, the correct answer is **28%**.