UPSC 2015 CDS II Math Paper

Let each side of the square be a unit.
Length of the rectangle =a+

30

100

a
=1.3a
Breadth of the rectangle
=a+

20

100

a=1.2a
Increase in the area
=1.3a×1.2a−a2=1.56a2−a2
=0.56a2
Therefore, the area of the resulting rectangle exceeds the area of the square by 56%.
Trick: The resulting area is increased by
=(30+20+

30×20

100

)%=56%