The average marks obtained by 150 students in an examination is 40. If the average marks of passed students is 60 and that of the failed students is 20, then what is the number of students who passed the examination?

Options

A. 25
B. 50
C. 75
D. 100

Answer

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

### Step 1: Understand the Problem
We know that:
- Total number of students = 150
- Average marks of all students = 40
- Average marks of passed students = 60
- Average marks of failed students = 20

### Step 2: Calculate Total Marks of All Students
The total marks obtained by all students can be calculated using the average:
\[ \text{Total Marks} = \text{Average} \times \text{Number of Students} = 40 \times 150 = 6000 \]

### Step 3: Let the Number of Passed Students be \(x\)
Let \(x\) be the number of students who passed the examination. Therefore, the number of failed students will be:
\[ \text{Number of Failed Students} = 150 - x \]

### Step 4: Calculate Total Marks of Passed Students
The total marks obtained by the passed students can be calculated as:
\[ \text{Total Marks of Passed Students} = \text{Average Marks of Passed Students} \times \text{Number of Passed Students} = 60 \times x = 60x \]

### Step 5: Calculate Total Marks of Failed Students
The total marks obtained by the failed students can be calculated as:
\[ \text{Total Marks of Failed Students} = \text{Average Marks of Failed Students} \times \text{Number of Failed Students} = 20 \times (150 - x) = 20(150 - x) = 3000 - 20x \]

### Step 6: Set Up the Equation
Since the total marks of all students is the sum of the total marks of passed and failed students, we can set up the equation:
\[ 6000 = 60x + (3000 - 20x) \]

### Step 7: Simplify the Equation
Now, simplify the equation:
\[ 6000 = 60x + 3000 - 20x \]
Combine like terms:
\[ 6000 = 40x + 3000 \]

### Step 8: Solve for \(x\)
Subtract 3000 from both sides:
\[ 6000 - 3000 = 40x \]
\[ 3000 = 40x \]
Now, divide both sides by 40:
\[ x = \frac{3000}{40} = 75 \]

### Conclusion
The number of students who passed the examination is \(75\).

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