If in a rectangle, the length is increased and breadth reduced each by 2 units, the area is reduced by 28 square units.

Solution:

Let the length and breadth of the rectangle be  and  units respectively

Then, area of rectangle  square units

If length is increased and breadth reduced each by  units, then the area is reduced by square units

$\begin{aligned} &(x+2)(y-2)=x y-28 \\ \Rightarrow & x y-2 x+2 y-4=x y-28 \\ \Rightarrow &-2 x+2 y-4+28=0 \\ \Rightarrow &-2 x+2 y+24=0 \\ \Rightarrow & 2 x-2 y-24=0 \end{aligned}$

Therefore, 

Then the length is reduced by  unit and breadth is increased by units then the area is increased by  square units

$(x-1)(y+2)=x y+33$

$\Rightarrow x y+2 x-y-2=x y+33$

$\Rightarrow 2 x-y-2-33=0$

 

$\Rightarrow 2 x-y-35=0$

Therefore, $2 x-y-35=0 \quad \ldots \ldots(i i)$

Thus we get the following system of linear equation

$2 x-2 y-24=0$

 

$2 x-y-35=0$

By using cross multiplication, we have

$\frac{x}{(-2 \times-35)-(-1 \times-24)}=\frac{y}{(2 \times-35)-(2 \times-24)}=\frac{1}{(2 \times-1)-(2 \times-2)}$

$\frac{x}{70-24}=\frac{-y}{-70+48}=\frac{1}{-2+4}$

$\frac{x}{46}=\frac{-y}{-22}=\frac{1}{2}$

$x=\frac{46}{2}$

$x=23$

and

$y=\frac{22}{2}$

$y=11$

The length of rectangle is units.

The breadth of rectangle is units.

Area of rectangle =lengthbreadth,

$=x \times y$

$=23 \times 11$

$=253$ square units

Hence, the area of rectangle is square units