A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2 of area. What is the area of the original rectangle in square meters?

The correct option is 2250.

To find the area of the original rectangle, we can set up system equations based on the relationships given in the problem statement.

Let $L$ represent the length of the original rectangle in meters, and let $B$ represent its breadth in meters.

The original area of the rectangle is given by:
$\text{Original Area}=L\times B$

Step 1: Set up the equation for the square.
When the length is reduced by 10 m, it becomes $L-10$.
When the breadth is reduced by 5 m, it becomes $B-5$.
Since these new dimensions form a square, they must be equal to each other:
$L-10=B-5$

Rearranging this equation gives:
$L=B+5$ (Equation 1)

Step 2: Set up the equation for the change in area.
The new area of the square is:
$\text{New Area}=(L-10)(B-5)$

We are told that the rectangle loses 650 m² of area during this process. Therefore:
$\text{Original Area}-\text{New Area}=650$

Substituting the area expressions into the equation:
$LB-(L-10)(B-5)=650$

Expand the product on the left-hand side:
$LB-(LB-5L-10B+50)=650$

Simplify the equation by canceling $LB$ and distributing the negative sign:
$5L+10B-50=650$

Add 50 to both sides of the equation:
$5L+10B=700$

Divide the entire equation by 5 to simplify:
$L+2B=140$ (Equation 2)

Step 3: Solve the system of equations.
Substitute the expression for $L$ from Equation 1 into Equation 2:
$(B+5)+2B=140$

Combine like terms:
$3B+5=140$

Subtract 5 from both sides:
$3B=135$

Divide by 3:
$B=45\text{m}$

Now, find $L$ using Equation 1:
$L=45+5=50\text{m}$

Step 4: Calculate the original area.
Using the original length and breadth, the area is:
$\text{Original Area}=50\times 45=2250{\text{m}}^2$

Thus, the area of the original rectangle is 2250 square meters.