The average marks obtained by 140 students in an examination is 90. If the average marks of passed students is 120 and the number of students who failed the examination are 90, then what is the average marks of students who failed the examination?

Options

A. 60
B. `73.33`
C. `85.66`
D. 88

Answer

To solve the problem step by step, we will follow the given information and use basic arithmetic operations.

### Step 1: Understand the given data
- Total number of students = 140
- Average marks of all students = 90
- Average marks of passed students = 120
- Number of students who failed = 90

### Step 2: Calculate the total marks obtained by all students
To find the total marks obtained by all students, we can use the formula:
\[ \text{Total Marks} = \text{Average Marks} \times \text{Total Students} \]
Substituting the values:
\[ \text{Total Marks} = 90 \times 140 = 12600 \]

### Step 3: Calculate the number of students who passed
Since the total number of students is 140 and the number of students who failed is 90, we can find the number of students who passed:
\[ \text{Number of Passed Students} = \text{Total Students} - \text{Number of Failed Students} \]
\[ \text{Number of Passed Students} = 140 - 90 = 50 \]

### Step 4: Calculate the total marks obtained by passed students
Using the average marks of passed students:
\[ \text{Total Marks of Passed Students} = \text{Average Marks of Passed Students} \times \text{Number of Passed Students} \]
Substituting the values:
\[ \text{Total Marks of Passed Students} = 120 \times 50 = 6000 \]

### Step 5: Calculate the total marks obtained by failed students
To find the total marks obtained by failed students, we subtract the total marks of passed students from the total marks of all students:
\[ \text{Total Marks of Failed Students} = \text{Total Marks} - \text{Total Marks of Passed Students} \]
\[ \text{Total Marks of Failed Students} = 12600 - 6000 = 6600 \]

### Step 6: Calculate the average marks of failed students
Now, we can find the average marks of failed students using the total marks obtained by failed students and the number of failed students:
\[ \text{Average Marks of Failed Students} = \frac{\text{Total Marks of Failed Students}}{\text{Number of Failed Students}} \]
Substituting the values:
\[ \text{Average Marks of Failed Students} = \frac{6600}{90} \approx 73.33 \]

### Final Answer
The average marks of students who failed the examination is approximately **73.33**.

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