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.

Let us denote the length of the original rectangle as _l and its breadth as _b.
The area of the original rectangle, _A, is given by the formula:
$$A=l\times b$$

According to the first condition, when the length is reduced by 10 m and the breadth by 5 m, the rectangle becomes a square. Since a square has equal sides, the new length and the new breadth must be equal:
$$l-10=b-5$$
Rearranging this equation, we get:
$$l-b=5\Rightarrow l=b+5$$ (Equation 1)

According to the second condition, during this reduction, the area of the rectangle decreases by 650 m². The new area is:
$$(l-10)(b-5)=lb-650$$

Let us expand the left side of the equation:
$$lb-5l-10b+50=lb-650$$
Subtracting $lb$ from both sides, we get:
$$-5l-10b+50=-650$$
Rearranging the terms:
$$5l+10b=700$$
Dividing the entire equation by 5 to simplify:
$$l+2b=140$$ (Equation 2)

Now, substitute the value of _l from Equation 1 ($l=b+5$) into Equation 2:
$$(b+5)+2b=140$$
Combine the terms containing _b:
$$3b+5=140$$
Subtract 5 from both sides:
$$3b=135$$
Divide by 3:
$$b=45\text{m}$$

Now, find the length _l using Equation 1:
$$l=45+5=50\text{m}$$

Finally, we calculate the area of the original rectangle:
$$A=l\times b=50\times 45=2250{\text{m}}^2$$