Question

there are two concentric circles on the playground. The diameter of the larger circle is 40% greater than the diameter of the smaller circle. The area of the larger circle is what percent greater than the area of the smaller circle

Answer 1

Let
D1-------------------- >diameter of the larger circle 
D2-------------------- >diameter of the smaller circle
D1=D2*1.4----------- > D2=D1/1.4

A1--------------- > Area of the larger circle 
A2--------------- > Area of the smaller circle 
A1=pi*D1²/4
A2=pi*D2²/4----------- > pi*D1²/(1.4² *4)-------- >A1/1.4²------ > A1*(0.51)
A2=0.51A1---------- > A1=A2/0.51=1.96 A2
A1=1.96A2

The answer is 
the area of the larger circle is 96%  greater than the area of the smaller circle