Question

In a class of 60 students 46 passed biology and 42 passed chemistry. Every student ls passed at least one of the two subjects. How many students passed in both subjects

Answer 1

Let's denote the following:

- \( n = 60 \) is the total number of students.
- \( A = 46 \) is the number of students who passed biology.
- \( B = 42 \) is the number of students who passed chemistry.
- \( x \) is the number of students who passed both subjects.

We can use the principle of inclusion-exclusion which states:

\[ |A \cup B| = |A| + |B| - |A \cap B| \]

Here:

- \( |A \cup B| \) is the number of students who passed at least one subject, which is given as 60 since every student passed at least one of the subjects.
- \( |A| = 46 \)
- \( |B| = 42 \)
- \( |A \cap B| = x \)

So, we set up the equation:

\[ 60 = 46 + 42 - x \]

Solving for \( x \):

\[ 60 = 88 - x \]
\[ x = 88 - 60 \]
\[ x = 28 \]

Thus, the number of students who passed both subjects is \( x = 28 \).