If the length of a rectangular field is doubled and its breadth is halved (i.e, reduced by 50% ) . What is percentage change in its area ?

Options

A. `0%`
B. `10%`
C. `25%`
D. `33.33%`

Answer

To solve the problem, we need to calculate the percentage change in the area of a rectangular field when its length is doubled and its breadth is halved.

### Step-by-Step Solution:

1. **Define the Original Dimensions:**
Let the original length of the rectangle be \( L \) and the original breadth be \( B \).

2. **Calculate the Original Area:**
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Breadth} \]
Therefore, the original area \( A_{original} \) is:
\[ A_{original} = L \times B \]

3. **Define the New Dimensions:**
According to the problem, the length is doubled and the breadth is halved:
- New length \( L_{new} = 2L \)
- New breadth \( B_{new} = \frac{B}{2} \)

4. **Calculate the New Area:**
The new area \( A_{new} \) is:
\[ A_{new} = L_{new} \times B_{new} = (2L) \times \left(\frac{B}{2}\right) \]
Simplifying this gives:
\[ A_{new} = 2L \times \frac{B}{2} = L \times B = A_{original} \]

5. **Calculate the Change in Area:**
The change in area is:
\[ \text{Change in Area} = A_{new} - A_{original} = (L \times B) - (L \times B) = 0 \]

6. **Calculate the Percentage Change in Area:**
The percentage change in area is calculated using the formula:
\[ \text{Percentage Change} = \left(\frac{\text{Change in Area}}{A_{original}}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage Change} = \left(\frac{0}{L \times B}\right) \times 100 = 0\% \]

### Conclusion:
The percentage change in the area of the rectangular field is **0%**.