Each side of a rectangular field is reduced by 40%. By how much percent is the area of the field diminished?

Let the length of rectangle be X units & breadth of rectangle be Y units.

We know that, Area of rectangle = length× breadth

⇒ Area of rectangular field= XY sq.units

Now, both length and breadth of rectangle are reduced by 40%

⇒ New length of rectangle = X – (40% of X) = 0.6X units

⇒ New breadth of rectangle = Y – (40% of Y) = 0.6Y units

New area of rectangular field= New length× New breadth

⇒ New area of rectangular field= 0.6X × 0.6Y = 0.36XY sq.units

Change in area= original area – new area = XY – 0.36XY= 0.64XY

∴% decrease in area $(= \frac{{0.64XY}}{{XY}} \times 100 = 64)$