The average marks obtained by 100 candidates in an examinatiion are 45. If the average marks of the passed students are 50 while the average marks of the failed students is 40. Then find the number of students who passes the examination.

Options

A. 30
B. 40
C. 50
D. 60

Explanation

To solve the problem step by step, we can follow these steps:

### Step 1: Define Variables
Let:
- \( p \) = number of students who passed the examination
- \( f \) = number of students who failed the examination

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of students is 100:
\[ p + f = 100 \quad \text{(Equation 1)} \]
2. The average marks of all students is 45, which gives us:
\[ \frac{(50p + 40f)}{100} = 45 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
Multiply both sides of Equation 2 by 100 to eliminate the fraction:
\[ 50p + 40f = 4500 \quad \text{(Equation 2 simplified)} \]

### Step 4: Express \( f \) in terms of \( p \)
From Equation 1, we can express \( f \) in terms of \( p \):
\[ f = 100 - p \quad \text{(Substituting into Equation 2)} \]

### Step 5: Substitute \( f \) into Equation 2
Substituting \( f \) into the simplified Equation 2:
\[ 50p + 40(100 - p) = 4500 \]
Expanding this gives:
\[ 50p + 4000 - 40p = 4500 \]

### Step 6: Combine Like Terms
Combine like terms:
\[ 10p + 4000 = 4500 \]

### Step 7: Solve for \( p \)
Subtract 4000 from both sides:
\[ 10p = 4500 - 4000 \]
\[ 10p = 500 \]
Dividing both sides by 10:
\[ p = 50 \]

### Step 8: Conclusion
The number of students who passed the examination is:
\[ \boxed{50} \]