Question

The area of a rectangle gets reduced by 80 sq units if its length is reduced by 5 units and the breadth is increased by 2 units. If we increase the length by 10 units and decrease the by 5 units, the area is increased by 50 sq units. Find the length and breadth of the rectangle.

• A. $l=40,b=30$
  
• B. $l=30,b=-10$
  
• C. $l=-40,b=-30$
  
• D. $l=10,b=-30$
  

Answer 1

The correct option is A $l=40,b=30$


Let length and Breadth be $l,b$

and the Area be $A=l\ast b.............\left(1\right)$

Now, According to Question

$A-80=(l-5)(b+2)\Rightarrow A-80=lb+2l-5b-10\Rightarrow 2l-5b=-\mathrm{70................}\left(2\right)$ (Since, A=l*b)

Similarly,

$A+50=(l+10)(b-5)\Rightarrow A+50=lb-5l+10b-50\Rightarrow 10b-5l=\mathrm{100..............}\left(3\right)$

Solving (2) and (3)

we get, $l=40,b=30$