The area of a rectangle gets reduced by 9 square units . . .

Question : The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Doubt by Noor

Solution : 

Let length of the rectangle be x units 

and breadth of the rectangle be y units

Area of rectangle = l×b
= xy square units. 

ATQ

(x-5)×(y+3)=(xy-9)
x(y+3)-5(y+3)=xy-9
xy+3x-5y-15=xy-9

3x-5y-15=-9

3x-5y=-9+15
3x-5y=6 — (1) 

Also

(x+3)×(y+2)=(xy+67)
x(y+2)+3(y+2)=xy+67
xy+2x+3y+6=xy+67
2x+3y+6=67
2x+3y=67-6
2x+3y=61 — (2) 

Solving equations (1) and (2) 

3x-5y=6

2x+3y=61

[3x-5y=6 ]×2

[2x+3y=61]×3

6x-10y=12

6x+9y=183
-   -       - 
-----------------
0x-19y=-171
-----------------

-19y=-128
19y=128
y=128/19
y=9

putting y=9 in equation (1) 
3x-5(9)=6
3x-45=6
3x=6+45
3x=51
x=51/3
x=17

Hence, length of rectangle is 17 units and breadth of rectangle is 9 units.