Each question has four options(A), (B), (C) and (D) for answers. Select the right answer and write in English letters in the box against each question in the enclosed answer sheet.
If the length of a rectangle is increased by 10% and its breadth is decreased by 10%, then its area

Options

A. decreases by 1 %
B. increases by 1 %
C. decreases by 2%
D. remains unchanged

Answer

To solve the problem of how the area of a rectangle changes when the length is increased by 10% and the breadth is decreased by 10%, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Initial Dimensions**:
- Let the initial length (L) of the rectangle be 100 units.
- Let the initial breadth (B) of the rectangle be 100 units.

2. **Calculate the Initial Area**:
- The area (A) of a rectangle is given by the formula:
\[ A = L \times B \]
- Substituting the values:
\[ A = 100 \times 100 = 10,000 \text{ square units} \]

3. **Calculate the New Length**:
- The length is increased by 10%. Therefore, the new length (L') is:
\[ L' = L + 0.1 \times L = 100 + 10 = 110 \text{ units} \]

4. **Calculate the New Breadth**:
- The breadth is decreased by 10%. Therefore, the new breadth (B') is:
\[ B' = B - 0.1 \times B = 100 - 10 = 90 \text{ units} \]

5. **Calculate the New Area**:
- The new area (A') is given by:
\[ A' = L' \times B' = 110 \times 90 \]
- Performing the multiplication:
\[ A' = 9900 \text{ square units} \]

6. **Determine the Change in Area**:
- The change in area can be calculated as:
\[ \text{Change} = A' - A = 9900 - 10,000 = -100 \]

7. **Calculate the Percentage Change**:
- The percentage change in area is calculated using the formula:
\[ \text{Percentage Change} = \frac{\text{Change}}{\text{Initial Area}} \times 100 \]
- Substituting the values:
\[ \text{Percentage Change} = \frac{-100}{10,000} \times 100 = -1\% \]

### Conclusion:
The area of the rectangle decreases by 1%. Therefore, the correct answer is **(A) decreased by 1%**.