jmc

Of the 40 who had heart trouble, 20 also had high blood pressure, so there are $40-20=20$ teachers who only have heart trouble. Similarly, there are $70-20=50$ teachers with only high blood pressure. So, of the 120 teachers total, there are $20+20+50=90$ teachers with one of these two maladies. That means $120-90=30$ teachers with neither, which is $\frac{30}{120}=\boxed{25\%}$ of the teachers.