In the diagram, two circles overlap. The area of the overlapped region is $\frac{3}{5}$ of the area of the small circle and $\frac{6}{25}$ of the area of the large circle. The ratio of the area of the small circle to the area of the large circle is
(A) $18: 125$
(B) $1: 3$
(C) $5: 12$
(D) $2: 5$
(E) $1: 4$

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-034.jpg?height=366&width=439&top_left_y=646&top_left_x=1293)
Suppose that $L$ is the area of the large circle, $S$ is the area of the small circle, and $A$ is the area of the overlapped region.

Since the area of the overlapped region is $\frac{3}{5}$ of the area of the small circle, then $A=\frac{3}{5} S$.

Since the area of the overlapped region is $\frac{6}{25}$ of the area of the large circle, then $A=\frac{6}{25} L$.

Therefore, $\frac{3}{5} S=\frac{6}{25} L$.

Multiplying both sides by 25 to clear denominators, we obtain $15 S=6 L$.

Dividing both sides by 3 , we obtain $5 S=2 L$. Therefore, $\frac{5 S}{L}=2$ or $\frac{S}{L}=\frac{2}{5}$.

This means that the ratio of the area of the small circle to the area of the large circle is $2: 5$.