Step 1: Understanding the Question:
The problem requires finding the overall percentage change in a rectangle's area after its length is increased by a certain percentage and its breadth is decreased by the same percentage.
Step 2: Key Formula or Approach:
Rectangle Area = \(\text{Length} \times \text{Breadth}\).
For consecutive percentage modifications \(x\) and \(y\), the net percentage change is found via the formula:
\[ \text{Net Change \%} = \left( x + y + \frac{x \times y}{100} \right) \% \]
Step 3: Detailed Explanation:
Assume the initial length is \(L\) and the initial breadth is \(B\).
Initial Area \(A = L \times B\).
A 10% length increase makes the new length \(1.1L\).
A 10% breadth decrease makes the new breadth \(0.9B\).
New Area \(A' = 1.1L \times 0.9B = 0.99LB\).
This shows the new area is 99% of the original, signifying a 1% reduction (\(100\% - 99\%\)).
Alternative method using the formula:
Assign \(x = +10\) (for increase) and \(y = -10\) (for decrease).
\[ \text{Net Change \%} = 10 - 10 + \frac{10 \times (-10)}{100} = 0 - \frac{100}{100} = -1\% \]
The negative result confirms a 1% decrease.
Step 4: Final Answer:
The correct choice is (B).