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What change in percent is made in the area of a rectangle by decreasing its length and increasing its breadth by 5%?

Options:

  1. 25% increase
  2. 2.5% decrease
  3. 0.25% increase
  4. 0.25% decrease

The correct Answer is Option 4. 0.25% decrease

Solution:

Let assume length of the rectangle = x sqm

Breadth of the rectangle = y sqm

Area of rectangle = length * breadth

Area of rectangle : XY sq. m

Length ‘ x’ decreased by 5% & breadth ‘y’ increase by 5%

New length = 0.95x meter

New breadth = 1.05y meter

New rectangle area : 0.95x*1.05y = 0.9975 sq. m

Change in Area = Original Area – New Area = xy – 0.9975xy = 0.0025 xy sqm

% decrease in area = (0.0025xy/xy)*100 = 0.25 % sqm

Ans : 0.25% decrease in area