The average marks of 120 students are 35 . If the average of passed students was 39 and failed students was 15 , then find the number of students who have passed .

Options

A. 80
B. 100
C. 120
D. 140

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given data
We know:
- Total number of students = 120
- Average marks of all students = 35
- Average marks of passed students = 39
- Average marks of failed students = 15

### Step 2: Set up variables
Let:
- \( x \) = number of students who passed
- \( 120 - x \) = number of students who failed

### Step 3: Use the formula for average
The formula for the overall average can be expressed as:
\[ \text{Overall Average} = \frac{(\text{Average of passed} \times \text{Number of passed}) + (\text{Average of failed} \times \text{Number of failed})}{\text{Total number of students}} \]
Substituting the known values:
\[ 35 = \frac{(39 \times x) + (15 \times (120 - x))}{120} \]

### Step 4: Multiply both sides by 120
To eliminate the denominator, multiply both sides by 120:
\[ 35 \times 120 = 39x + 15(120 - x) \]
Calculating \( 35 \times 120 \):
\[ 4200 = 39x + 1800 - 15x \]

### Step 5: Simplify the equation
Combine like terms:
\[ 4200 = 39x - 15x + 1800 \]
\[ 4200 = 24x + 1800 \]

### Step 6: Isolate \( x \)
Subtract 1800 from both sides:
\[ 4200 - 1800 = 24x \]
\[ 2400 = 24x \]

### Step 7: Solve for \( x \)
Divide both sides by 24:
\[ x = \frac{2400}{24} = 100 \]

### Conclusion
The number of students who have passed is \( \boxed{100} \).

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