A rectangle becomes a square when its length is reduced by 10 units and its breadth is increased by 5 units. but by this process the area of the rectangle is reduced by 210 sq.units. The area of the rectangle (A) in square units is :

Answer: Option D

Let the length and breadth of the rectangle be $$l$$ and b respectively
$$\begin{array}{rl}& l-10=b+5\\ & \Rightarrow l-b=\mathrm{15.....}(i)\\ & \text{And,}\\ & \Rightarrow lb-\left(l-10\right)\left(b+5\right)=210\\ & \Rightarrow lb-\left(lb+5l-10b-50\right)=210\\ & \Rightarrow -5l+10b=160\\ & \Rightarrow -l+2b=\mathrm{32.....}(ii)\end{array}$$
Adding (i) and (ii), we get : b = 47
Putting b = 47 in equation (i), we get $$l$$ = 62
Hence, area of the rectangle :
= $$lb$$
= (62 × 47) sq.units
= 2914 sq.units
Clearly, 2925 > A > 2900