The make-up exam failed 20%, 15x20%=3 people, and failed again. The rest 12 people passed the make-up exam.
Those three idiots failed in the end. So the final pass rate is (150-3)/150 x100% = 98%.
Comprehensive formula calculation:
[ 150- 150 x( 1-90%)x20 %]/ 150 x 100% = 98%
Answer: The final pass rate is 98%.