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 step by step, we will follow these calculations:

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

### Step 2: Calculate the new length after a 50% increase
The new length \( L' \) after a 50% increase can be calculated as:
\[ L' = L + 0.5L = 1.5L \]

### Step 3: Calculate the new breadth after a 20% decrease
The new breadth \( B' \) after a 20% decrease can be calculated as:
\[ B' = B - 0.2B = 0.8B \]

### Step 4: Calculate the original area of the rectangle
The original area \( A \) of the rectangle is given by:
\[ A = L \times B \]

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

### Step 6: Calculate the change in area
The change in area \( \Delta A \) is:
\[ \Delta A = A' - A = 1.2LB - LB = 0.2LB \]

### Step 7: Calculate the percentage change in area
The percentage change in area can be calculated using the formula:
\[ \text{Percentage Change} = \left( \frac{\Delta A}{A} \right) \times 100 = \left( \frac{0.2LB}{LB} \right) \times 100 = 20\% \]

### Conclusion
The percentage change in the area of the rectangle is an increase of **20%**.

---