In an examination `72%` of the students passed in physics `48%` of the students passed in biology and every student passed in at least one subject. How many students passed in both subjects.

Options

A. `80%`
B. `75%`
C. `20%`
D. `25%`

Answer

To solve the problem step by step, we can use the principle of inclusion-exclusion in set theory. Here’s how we can approach it:

### Step 1: Define the Variables
Let:
- \( P \) = Percentage of students who passed in Physics = 72%
- \( B \) = Percentage of students who passed in Biology = 48%
- \( X \) = Percentage of students who passed in both subjects

### Step 2: Use the Inclusion-Exclusion Principle
According to the principle of inclusion-exclusion, the total percentage of students who passed in at least one subject can be expressed as:
\[ P + B - X = 100\% \]
This equation accounts for the students who passed in both subjects being counted twice.

### Step 3: Substitute the Known Values
Substituting the known values into the equation:
\[ 72\% + 48\% - X = 100\% \]

### Step 4: Simplify the Equation
Now, simplify the equation:
\[ 120\% - X = 100\% \]

### Step 5: Solve for \( X \)
Rearranging the equation to solve for \( X \):
\[ X = 120\% - 100\% \]
\[ X = 20\% \]

### Conclusion
Thus, the percentage of students who passed in both subjects is \( 20\% \).

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