Let $B\left(\frac{33}{5}, \frac{28}{5}, \frac{38}{5}\right)$ divides $\overline{A C}$ in the ratio $k: 1$, where $A(3,2,4)$ an $d C(9,8,10)$.


Now,
$$
\begin{aligned}
& \Rightarrow \quad 45 k+15=33 k+33 \\
& \Rightarrow \quad 12 k=18 \\
& \therefore \quad k=\frac{3}{2} \\
& \text { and } \\
& \Rightarrow \\
& \Rightarrow \\
& \Rightarrow \\
& \text { and } \\
& \Rightarrow \\
& \Rightarrow \\
& \Rightarrow \\
& \frac{8 k+2}{k+1}=\frac{28}{5} \\
& 40 k+10=28 k+28 \\
& 12 k=18 \\
& k=\frac{3}{2} \\
& \frac{10 k+4}{k+1}=\frac{38}{5} \\
& 50 k+20=38 k+38 \\
& 12 k=18 \\
& k=\frac{3}{2} \\
&
\end{aligned}
$$
From Eqs. (i), (ii) and (iii), we get
$$
k=\frac{3}{2}
$$
Now, $\quad k: 1=\frac{3}{2}: 1=3: 2$