We have two responses for you

Hi,

80% of the students in the class are business majors. 80% of 40 is 0.80 × 40 = 32 and hence there are 32 business majors and 40 - 32 = 8 students who are not business majors.

75% of the 24 who passed the exam are business majors. 75% of 24 is 0.75 × 24 = 18 so 18 business majors passed the exam and 24 - 18 = 6 non business majors passes the exam.

6 is what percentage of 8?

Penny

In fact, the question has nothing to do with percentages:

In a class of 40 students, 32 are business majors. Of the 24 students who passed the mid-term examination, 18 are business majors. How many students in the class who are not business majors passed the examination?

The use of percentages in this context makes the question sound more complicated to some, and detracts from the fact that it is just about elementary arithmetic. The same effect would be achieved by asking the question in a foreign language
(say french):

Dans une classe de 40 étudiants, 32 étudient en administration des affaires.
Des 24 étudiants qui ont réussi l'examen intrasemestriel, 18 sont en
administration des affaires. Combien d'étudiants de la classe qui ne sont pas en
administration des affaires ont réussi l'examen?

The basic role of percentages (and communication tools in general) is to simplify complex information. If I want to be understood rather than confusing, I say that 27 of my 35 students passed the exam rather than say that the success rate was 77.1%. However with larger numbers, percentages give a better, simpler view: I would rather read that in the last election, voter turnout was 53% rather than to read that 4,421,628 of the 8,380,702 voters did vote; the latter formulation is still understandable though it is cumbersome. In our society, the people are so much bombarded by senseless data in the most complex form possible that they become innumerate. We then arrive at the paradoxical situation where percentages are tought at school and universities, though people should easily understand them by themselves in the
first place, and these lessons on percentages take away time for lessons about simple numbers and simple arithmetic, which are much needed.

Claude