Let the point $P(11,15)$divide the line segment $A=(15,5)$ and $B=(9,20)$ in ratio $m_1:m_2$

$$\begin{gathered} A=(15,5)?x_1=15,y_1=5 \\ B+(9,20)?x_2=9,y_2=20 \\ P=(11,15)?x=11,y=15 \end{gathered}$$

So by formula,

$$\begin{gathered} x=\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2} \\ ?11=\frac{9m_1+15m_2}{m_1+m_2} \\ ?11(m_1+m_2)=9m_1+15m_2 \\ ?11m_1+11m_2=9m_1+15m_2 \\ ?11m_1-9m_1=15m_2-11m_2 \\ ?2m_1=4m_2 \\ \frac{m_1}{m_2}=\frac{4}{2} \\ \frac{m_1}{m_2}=\frac{2}{1} \end{gathered}$$

The ratio is $2:1$