75% of the students passed in an examination. If 2 more students had passed the examination. 80% would have been successful. How many students are there in the class?

Options

A. 40
B. 30
C. 50
D. 32

Answer

To solve the problem step by step, let's denote the total number of students in the class as \( x \).

### Step 1: Set up the equation based on the information given.
According to the problem, 75% of the students passed the examination. Therefore, the number of students who passed is:
\[ \text{Number of students who passed} = \frac{75}{100} \times x = \frac{3}{4}x \]

If 2 more students had passed, then the number of students who passed would be:
\[ \frac{3}{4}x + 2 \]

### Step 2: Set up the equation for the new passing percentage.
If 80% of the students had passed, then the number of students who would have passed is:
\[ \text{Number of students who would pass} = \frac{80}{100} \times x = \frac{4}{5}x \]

### Step 3: Create the equation.
According to the problem, if 2 more students passed, the number of students who passed would equal the number of students who would have passed if 80% had passed:
\[ \frac{3}{4}x + 2 = \frac{4}{5}x \]

### Step 4: Solve the equation.
To eliminate the fractions, we can multiply the entire equation by 20 (the least common multiple of 4 and 5):
\[ 20\left(\frac{3}{4}x\right) + 20(2) = 20\left(\frac{4}{5}x\right) \]
This simplifies to:
\[ 15x + 40 = 16x \]

### Step 5: Rearrange the equation to isolate \( x \).
Subtract \( 15x \) from both sides:
\[ 40 = 16x - 15x \]
This simplifies to:
\[ 40 = x \]

### Step 6: Conclusion.
Thus, the total number of students in the class is:
\[ \boxed{40} \]