When 5040 is divided by 65, 55 and 45, it can only be divided by 45, that is, 5040/45= 1 12.

Therefore, there are 1 12 people in the two tour groups.

Divide 6570 by 65 and 55, and neither can be divided. Therefore, when Party A and Party B buy tickets separately, it is impossible to buy tickets with the same price.

Suppose the number of people in a group is X, which is above 100; The other group has less than 50 people.

45x+65( 1 12-x)=6570

X=35.5 is irrelevant.

Suppose the number of people in a group is X, which is between 50- 100; The other group has less than 50 people.

55x+65( 1 12-x)=6570

x=7 1

Therefore, the number of Party A and Party B is 7 1, and the number of the other group is 4 1.