If the length of a rectangular field is increased by 20% and the breadth is reduced by 20%, the area of the rectangle will be `192 m^2` . What is the area of the original rectangle?

Options

A. `184m^2`
B. `196m^2`
C. `204 m^2`
D. None of these

Explanation

To find the area of the original rectangle, we can follow these steps:

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

### Step 2: Calculate the new dimensions
According to the problem:
- The length is increased by 20%. Therefore, the new length \( L' \) can be calculated as:
\[ L' = L + 0.2L = 1.2L \]
- The breadth is reduced by 20%. Therefore, the new breadth \( B' \) can be calculated as:
\[ B' = B - 0.2B = 0.8B \]

### Step 3: Calculate the area of the modified rectangle
The area of the modified rectangle is given as 192 m². We can express this area in terms of the new dimensions:
\[ \text{Area} = L' \times B' = (1.2L) \times (0.8B) \]
This simplifies to:
\[ \text{Area} = 0.96LB \]

### Step 4: Set up the equation
We know that this area equals 192 m²:
\[ 0.96LB = 192 \]

### Step 5: Solve for \( LB \)
To find \( LB \), we can rearrange the equation:
\[ LB = \frac{192}{0.96} \]
Calculating this gives:
\[ LB = 200 \text{ m}^2 \]

### Step 6: Conclusion
The area of the original rectangle is \( 200 \text{ m}^2 \).