Final answer:
Using set theory, it is estimated that 9 teachers might teach both Chemistry and Physics, and there are 6 teachers who teach only Physics in the secondary school.
Step-by-step explanation:
In a secondary school of 60 teachers, we have 30 teaching Mathematics, 27 teaching Physics, and 21 teaching Chemistry. It's given that 12 teach Mathematics and Physics, and none teaches both Mathematics and Chemistry. To answer the questions, we need to use principles of set theory to find the overlap and unique members of the sets.
(i) How many teach Chemistry and Physics?
We are given no specific number of teachers teaching both Chemistry and Physics. However, we can infer that since none teach both Mathematics and Chemistry, and 12 teach Mathematics and Physics, the remaining teachers who teach Physics (27 total - 12 Math/Physics) could potentially teach Chemistry. Given there are 21 Chemistry teachers, the maximum overlap for Chemistry and Physics would be the lesser of the two numbers, which is 21 - 12 = 9 teachers.
(ii) How many teach only Physics?
To find those who teach only Physics, we would subtract the number of teachers who teach Physics and another subject from the total number of Physics teachers. As we already accounted for 12 teaching Math and Physics, and potentially 9 teaching Chemistry and Physics, that leaves us 27 - (12 + 9) = 6 teachers who teach only Physics.