There is a rectangular plot the area of a rectangular plot gets reduced by 9 square metres if its length is reduced by 5 metres and breadth is increased by 3 metres if there is an increase in length by 3 metres and breadth by 2 metres then area of rectangular plot is increased by 67 meter sq
what is area of retangular plot?

Options

A. 125 metres square
B. 153 metressquare
C. 95 metres square
D. 140 metres square

Answer

To solve the problem, we will denote the original length and breadth of the rectangular plot as \( L \) and \( B \) respectively. We will set up equations based on the information given in the problem.

### Step 1: Set up the equations based on the area changes

1. **First Condition**: When the length is reduced by 5 meters and the breadth is increased by 3 meters, the area decreases by 9 square meters.
\[ (L - 5)(B + 3) = LB - 9 \]

2. **Second Condition**: When the length is increased by 3 meters and the breadth is increased by 2 meters, the area increases by 67 square meters.
\[ (L + 3)(B + 2) = LB + 67 \]

### Step 2: Expand both equations

1. **Expanding the first equation**:
\[ LB + 3L - 5B - 15 = LB - 9 \]
Simplifying this gives:
\[ 3L - 5B - 15 = -9 \implies 3L - 5B = 6 \quad \text{(Equation 1)} \]

2. **Expanding the second equation**:
\[ LB + 2L + 3B + 6 = LB + 67 \]
Simplifying this gives:
\[ 2L + 3B + 6 = 67 \implies 2L + 3B = 61 \quad \text{(Equation 2)} \]

### Step 3: Solve the system of equations

We now have a system of linear equations:
1. \( 3L - 5B = 6 \) (Equation 1)
2. \( 2L + 3B = 61 \) (Equation 2)

We can solve these equations using substitution or elimination. Here, we will use the elimination method.

1. Multiply Equation 2 by 5:
\[ 10L + 15B = 305 \quad \text{(Equation 3)} \]

2. Multiply Equation 1 by 3:
\[ 9L - 15B = 18 \quad \text{(Equation 4)} \]

3. Add Equations 3 and 4:
\[ (10L + 15B) + (9L - 15B) = 305 + 18 \]
This simplifies to:
\[ 19L = 323 \implies L = \frac{323}{19} = 17 \]

### Step 4: Substitute back to find \( B \)

Now that we have \( L = 17 \), substitute it back into Equation 2 to find \( B \):
\[ 2(17) + 3B = 61 \]
\[ 34 + 3B = 61 \implies 3B = 27 \implies B = 9 \]

### Step 5: Calculate the area of the rectangular plot

The area \( A \) of the rectangular plot is given by:
\[ A = L \times B = 17 \times 9 = 153 \text{ square meters} \]

### Final Answer
The area of the rectangular plot is **153 square meters**.

---