Haz, are you sure your working is correct?

If there are really 45 pupils in both classes, then there would be 30 pupils in classroom A and 15 pupils in classroom B.

Transferring 12 students from classroom B to classroom A results in classroom A having 42 pupils and classroom B having 3 pupils. That's not a ratio 4 : 1.

When 12 pupils move from classroom B to classroom A, two things happen at the same time
- classroom A gains 12 pupils
- classroom B loses 12 pupils

Classroom A already has 15 more pupils than classroom B. If you draw the models correctly, the gap will widen to 15 + 12 + 12 = 39 pupils. This is where Haz's workings are flawed.

Now classroom A has 39 more pupils than classroom B. This corresponds to the 3 units difference (from the ratio 4 : 1).

3 units --> 39
1 unit --> 13
5 units --> 65

There are 65 pupils in both classes at first, with 40 pupils in classroom A and 25 pupils in classroom B.