If length of the rectangle is increased by 50% and breadth is decreased by 20%. Then, what is the percentage change in the area?

Options

A. 20% decrease
B. 20% increase
C. 80% increase
D. None of these

Answer

To solve the problem of finding the percentage change in the area of a rectangle when its length is increased by 50% and its breadth is decreased by 20%, we can follow these steps:

### 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 New Length**:
The length is increased by 50%. Therefore, the new length \( L' \) can be calculated as:
\[ L' = L + 0.5L = 1.5L \]

3. **Calculate the New Breadth**:
The breadth is decreased by 20%. Therefore, the new breadth \( B' \) can be calculated as:
\[ B' = B - 0.2B = 0.8B \]

4. **Calculate the Original Area**:
The original area \( A \) of the rectangle is given by:
\[ A = L \times B \]

5. **Calculate the New Area**:
The new area \( A' \) of the rectangle with the new dimensions is:
\[ A' = L' \times B' = (1.5L) \times (0.8B) = 1.2LB \]

6. **Calculate the Change in Area**:
The change in area can be calculated as:
\[ \text{Change in Area} = A' - A = 1.2LB - LB = 0.2LB \]

7. **Calculate the Percentage Change in Area**:
The percentage change in area is given by:
\[ \text{Percentage Change} = \left( \frac{\text{Change in Area}}{\text{Original Area}} \right) \times 100 = \left( \frac{0.2LB}{LB} \right) \times 100 = 20\% \]

Thus, the percentage change in the area of the rectangle is **20% increase**.