Answer

Theorem: The bisector of an angle of a triangle divides the side opposite to the angle in the ratio of the remaining sides.
And $\because NQ$ is angle bisector of $\angle N$
$\begin{array}{l}
\Rightarrow \frac{ MQ }{ QP }=\frac{ MN }{ NP } \\
\Rightarrow \frac{14}{ QP }=\frac{25}{40} \\
\Rightarrow Q P=\frac{14 \times 4 0}{25} \\
\Rightarrow Q P=22.4
\end{array}$

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