Before 13 years, what it would be ?

Let Paul's age be $P$ , his wife's age be $W$ and their sons' ages be $S_{1}$ and $S_{2}$ , respectively.
It is given that : $P \times W + S_{1}+S_{2}=2011$ $W=P-1$ $S_{2}=S_{1}-1$

Combining those equations gives : $P (P-1)+2 \times S_{1}-1=2011$

The oldest Paul can be is 45 since $P(P-1)>2011$ for $P>45$ . We know Paul's children are younger than him, so $S_{1}<45$ .

So, rearranging the big equation gives: $S_{1}=\dfrac{2012-P(P-1)}{2}$

And then combining that with the inequality, $\dfrac{2012-P(P-1)}{2}<45 \to 1922<P(P-1)$ which occurs when $P \ge 45$ . So, then P = 45, Solving for $S_{1}$ gives $S_{1}=16$ .

= $P=45-13=32$ and $S_{1}= 16-13=3$ .

= $32(31) + 3(2)-1=997$