If the length of a rectangle is increased by 50% and breadth is decreased by 25%, what is the percentage change in its area?

### Concept & Successive Percentage Change When the two dimensions of a rectangle change by certain percentages, the net percentage change in its area can be found using the successive change formula. $$ Net Change = x + y + \frac{x y}{100} $$ ### Step-by-Step Solution * Let $x$ be the percentage change in length and $y$ be the percentage change in breadth. * The length increases by 50%, so $x = +50$. The breadth decreases by 25%, so $y = -25$. * Substitute these values into the formula: $$ Net Change = 50 - 25 + \frac{(50)(-25)}{100} $$ * Simplify the expression: $$ Net Change = 25 - \frac{1250}{100} = 25 - 12.5 = +12.5\% $$ * Since the result is positive, the area increases. ### Exam Strategy & Shortcut Assume the original length and breadth are both 10, giving an initial area of $10 \times 10 = 100$. A 50% increase in length makes it 15. A 25% decrease in breadth makes it 7.5. New Area = $15 \times 7.5 = 112.5$. Moving from 100 to 112.5 is exactly a 12.5% increase. ### Common Pitfall Students often simply add or subtract the given percentages ($50 - 25 = 25\%$), forgetting that area is a product of two dimensions and requires the successive change calculation. ### Final Answer Therefore, the correct answer is **12.5% increase**.