G10.4 If $P, Q$ are positive integers such that $P+Q+P Q=90$ and $D=P+Q$, find $D$. (Hint: Factorise $1+P+Q+P Q$ )
WLOG assume $P \leq Q, 1+P+Q+P Q=91$
$$
\begin{array}{l}
(1+P)(1+Q)=1 \times 91=7 \times 13 \\
1+P=1 \Rightarrow P=0 \text { (rejected) }
\end{array}
$$
or $1+P=7 \Rightarrow P=6$
$$
\begin{array}{l}
1+Q=13 \Rightarrow Q=12 \\
D=6+12=18
\end{array}
$$