Assume that the length of the rectangle is increased by 25% and the width is decreased by x% such that there is no change in the area of the rectangle. The value of x is ________.
Answers
Given : Length of the rectangle is increased by 25% and the width is decreased by x% such that there is no change in the area of the rectangle.
To find : Value of x
Solution :
Let length of rectangle be a and it's breadth be b .
It's Area is given by Length times breadth = ab sq. units .
Length after increment :-
=> (25% of a) + a
=> 25a/100 + a
=> 125 a/ 100
Breadth after decrement :-
=> b - ( x% of b )
=> b - bx / 100
=> ( 100 b - bx ) / 100
Area of rectangle after change in length and breadth :-
- 125a / 100 × ( 100 b - bx ) / 100
According to the question, area remains same.
So,
=> 125a / 100 × ( 100 b - bx ) / 100 = ab
=> (12500 ab-125 abx ) / 10000 = ab
By cross multiplication, we get :-
=> 12500 ab - 125 abx = 10000 ab
=> 12500 ab - 10000 ab = 125 abx
=> 2500 ab = 125 abx
=> 2500 / 125 = x
=> 20 = x
So the required value of x is 20.