$17 \cdot 165$ As shown in the figure, in $\triangle A B C$, $D E / / B C$, and $S_{\triangle A D E}: S_{\triangle C D E}=1: 3$. Then $S_{\triangle A D E}: S_{\triangle D B C}$ equals
(A) $1: 5$.
(B) $1: 12$.
(C) $1: 8$.
(D) $1: 9$.
(China Sichuan Province Junior High School Mathematics Competition, 1990)
[Solution] Given $S_{\triangle A D E}: S_{\triangle C D E}=1: 3$, then
$$
A E: E C=1: 3 \text {. }
$$

Also, $D E / / B C$, so $\triangle A D E \sim \triangle A B C$.
Thus, $S_{\triangle A D E}: S_{\triangle A B C}=1^{2}:(1+3)^{2}=1: 16$.
Therefore, $S_{\triangle A D E}: S_{\triangle D B C}=1:(16-1-3)=1: 12$.
Hence, the answer is $(B)$.