Question

The length of a rectangle is first increased by 10% then decreased by 5%. Find net percentage change on the area.

Answer 1

By 9.09

Let us assume the length of the rectangle is x and breadth is y. This makes the area of the rectangle x⋅y. Now, as mentioned, you have increased the length by 10 which makes it 1.1⋅x.

You want to maintain the area at x⋅y.

Length is 1.1⋅x.

So the breadth has to be 11.1 so that it maintains the area
=>(1.1⋅x)⋅(11.1⋅y)=x⋅y

11.1 is 0.909090...
so the breadth is reduced by 1−0.909090...) which is 0.090909...
this is percentage terms is 9.0909...