If the length of a rectangular plot of land is increased by 5% and the breadth decreased by 10%, by how much will its area change?

Options

A. increase by 5.5%
B. decrease by 5.5%
C. decrease by 0.55%
D. No change

Answer

To find the change in the area of a rectangular plot of land when the length is increased by 5% and the breadth is decreased by 10%, we can follow these steps:

### Step 1: Define the original dimensions
Let the original length of the rectangular plot be \( L \) and the original breadth be \( B \).

### Step 2: Calculate the new dimensions
- The new length after a 5% increase:
\[ \text{New Length} = L + 0.05L = 1.05L \]
- The new breadth after a 10% decrease:
\[ \text{New Breadth} = B - 0.10B = 0.90B \]

### Step 3: Calculate the original area
The original area \( A \) of the rectangle is given by:
\[ A = L \times B \]

### Step 4: Calculate the new area
The new area \( A' \) after the changes in dimensions is:
\[ A' = \text{New Length} \times \text{New Breadth} = (1.05L) \times (0.90B) \]
\[ A' = 0.945LB \]

### Step 5: Calculate the change in area
To find the change in area, we can subtract the original area from the new area:
\[ \text{Change in Area} = A' - A = 0.945LB - LB \]
\[ \text{Change in Area} = (0.945 - 1)LB = -0.055LB \]

### Step 6: Calculate the percentage change
To find the percentage change in area:
\[ \text{Percentage Change} = \left(\frac{\text{Change in Area}}{\text{Original Area}}\right) \times 100 \]
\[ \text{Percentage Change} = \left(\frac{-0.055LB}{LB}\right) \times 100 = -5.5\% \]

### Conclusion
The area of the rectangular plot decreases by 5.5%.

---