Points $K$ and $M$ are located on the sides $AB$ and $BC$ of triangle $ABC$, such that $BK: KA=1: 4, BM: MC=3: 2$. Lines $MK$ and $AC$ intersect at point $N$.

Find the ratio $AC: CN$.
Through point $M$, draw a line parallel to $A B$ until it intersects $A C$ at point $L$. From the similarity of triangles $L M C$ and $A B C$, we find that $A L=3 / 5 A B$, and $L M=2 / 5 A B=1 / 2 A K$. Therefore, $M L$ is the midline of triangle $A N K$, and

$A N=2 A L=6 / 5 A C$.

## Answer

$5: 1$.

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