10,11

A plane intersects the edges $A B, A C, D C$ and $D B$ of the tetrahedron $A B C D$ at points $M, N, P$ and $Q$ respectively, such that $A M$ : $M B=m, A N: N C=n, D P: P C=p$. Find the ratio $B Q / Q D$.
If the line $N P$ is parallel to the line $A D$, then $N P$ is parallel to the plane $A B D$. In this case, the intersecting plane intersects the plane $A B D$ along the line $M Q$, which is parallel to the line $N P$, so $B Q: Q D=B M: M A=1: m$.

Now let the line $N P$ intersect the line $A D$ at a point $T$ lying on the extension of the edge $A D$ beyond point $D$. Then the line $M T$ intersects the edge $B D$ at point $Q$.

Consider the plane of triangle $A D C$. Draw a line through vertex $C$ parallel to $A D$. Let $L$ be the point of intersection of this line with the line $N P$. From the similarity of triangles $C L P$ and $D T P$, it follows that

$$
C L=D T \cdot C P / P D=D T / p
$$

and from the similarity of triangles $C L N$ and $A T N$,

$$
A T=C L \cdot A N / N C=C L \cdot n=D T \cdot n / p
$$

Now consider the plane of triangle $A B D$. Draw a line through vertex $B$ parallel to $A D$, and extend $T M$ until it intersects this line at point $E$. From the similarity of triangles $A M T$ and $B M E$, we find that

$$
B E=A T \cdot B M / A M=A T / m,
$$

and from the similarity of triangles $T Q D$ and $E Q B$,

$$
B Q / Q D=B E / D T=(A T / m) / D T=(D T \cdot n /(p m)) / D T=n /(m p) .
$$

## Problem

Translate the above text into English, please retain the original text's line breaks and formatting, and output the translation result directly.