You are right brother that 360/12= 30. It means that you are dividing whole 360 degrees into 12 equal chunks. Now while your clock moves from 10 to 25 then it means that you clock covered three chunks (10-15, 15-20 and 20-25). So you have to multiply by 3 not by 1.5 and in this way you answer is 90 not 45.
Looking into other way round i.e you method. You divided 360 degree into 12 chunks but then multiplied by 1.5 as if you have divided (360) into 60 equal chunks and I don't know why you divided it by 10 (15/10=1.5) and then multiplied it.
One of the member mentioned that 360/60=6 and as clock has moved 15 chunks (in this case) so 6X15=90.
Another reason for 90: Let suppose that clock started from 15 (10+5) and ended 30 (25+5) now every one can say that angle is 90 no 45.
I think now it's clear that it was 90 and only 90 there is no sense of 45 left