II. (25 points) A group purchases tickets to a park, with ticket prices as shown in Table 1:
Table 1
\begin{tabular}{|c|c|c|c|}
\hline Number of ticket buyers & $1 \sim 50$ & $51 \sim 100$ & Over 100 \\
\hline Price per ticket & 13 yuan & 11 yuan & 9 yuan \\
\hline
\end{tabular}

There are two tour groups, Group A and Group B. If they purchase tickets separately, the total cost for both groups is 1314 yuan. If they purchase tickets together as one group, the total cost is 1008 yuan. How many people are in each of the two tour groups?
If the number of people does not exceed 100, the cost is at most 1300 yuan, so the total number of people in the two tour groups exceeds 100.
Also, $1008 \div 9=112$, so the total number of people in the two tour groups is 112.
Let the number of people in the two tour groups be $x$ and $y$ respectively. From $x+y=112$, we know that at least one of $x$ and $y$ is greater than 50. Also, since $112 \times 11=1232<1314$, it can be concluded that $x$ and $y$ cannot both be greater than 50.

If one tour group has more than 100 people and the other has fewer than 12 people, the total cost of tickets would be at most
$$
900+13 \times 12=1056<1314 \text{. }
$$

Therefore, it can be determined that one tour group has no more than 50 people, and the other has more than 50 but no more than 100 people.
Assume $1 \leqslant x \leqslant 50, 51 \leqslant y \leqslant 100$, then we have
$$
\left\{\begin{array}{l}
x+y=112, \\
13 x+11 y=1314 .
\end{array}\right.
$$

Solving this, we get $x=41, y=71$.
Therefore, the number of people in the two tour groups are 41 and 71 respectively.