Pair each boy with 1 girl first. There are 4 remaining girls who remain unpaired/with no partner.
69.5 - 65 = 4.5
To raise the average score of their girl partner from 65 to 69.5, each boy has to 'donate' 4.5 marks to their partner.
75 - 4.5 = 70.5
70.5 - 69.5 = 1
After 'donating', each boy has 70.5 marks left. That's 1 mark more than the class average. So each boy has 1 more mark left to 'donate' such that their own average score becomes 69.5 .
Now, there are 4 girls who have no partners. Each girl needs 4.5 marks more to raise their average to 69.5 .
So 4 girls need 4 x 4.5 = 18 marks more
Since each boy can 'donate' 1 more mark,
18 boys are needed to donate 18 marks.
This tells us that there are actually 18 boys. So number of girls = 18 + 4 = 22