In a class of 60 students, the number of students who passed biology is 6 more than the number who passed chemistry. Every student passed at least one of the two subjects and 8 students passed both subjects.

I) how many students passed biology?
ii) how many students passed chemistry?
iii) how many students passed only one subject?

yes

To answer these questions, we can use a concept called set theory. Let's break down the given information step by step.

Step 1: Identify the given information:
- Total number of students in the class = 60
- The number of students who passed both biology and chemistry = 8
- The number of students who passed biology is 6 more than the number who passed chemistry.

Step 2: Assign variables and create equations:
Let's assume that the number of students who passed chemistry is x. Therefore, the number of students who passed biology would be x + 6.
We can also calculate the number of students who passed at least one subject by adding the individual subjects and subtracting the overlap (students who passed both).
Total students passed at least one subject = (students passed chemistry) + (students passed biology) - (students passed both)
Total students passed at least one subject = x + (x + 6) - 8 = 2x - 2.

Step 3: Solve for the variables:
We know that the total number of students passed at least one subject is equal to the total number of students in the class.
Therefore, 2x - 2 = 60.

Simplifying the equation, we have:
2x = 62
x = 31

Step 4: Calculate the answers to each question:
I) The number of students who passed biology = x + 6 = 31 + 6 = 37.
ii) The number of students who passed chemistry = x = 31.
iii) The number of students who passed only one subject can be calculated by subtracting the number of students who passed both subjects from the total number of students who passed at least one subject.
Number of students passed only one subject = Total number of students passed at least one subject - Number of students passed both subjects
Number of students passed only one subject = (2x - 2) - 8
Number of students passed only one subject = (2 * 31 - 2) - 8
Number of students passed only one subject = 54 - 8
Number of students passed only one subject = 46.

Therefore, the number of students who passed only one subject is 46.