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 :

Solution (By Examveda Team)

Let the length and breadth of the rectangle be $$l$$ and b respectively
$$\eqalign{ & l - 10 = b + 5 \cr & \Rightarrow l - b = 15.....(i) \cr & {\text{And,}} \cr & \Rightarrow lb - \left( {l - 10} \right)\left( {b + 5} \right) = 210 \cr & \Rightarrow lb - \left( {lb + 5l - 10b - 50} \right) = 210 \cr & \Rightarrow - 5l + 10b = 160 \cr & \Rightarrow - l + 2b = 32.....(ii) \cr} $$
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