In an examination it is required to get 65% of the aggregate marks to pass. A student gets 684 marks and is declared failed by 8% marks. What are the maximum aggregate marks a student can get ?

Options

A. 950
B. 1200
C. 1050
D. Cannot be determined

Answer

To find the maximum aggregate marks a student can get, we can follow these steps:

### Step 1: Understand the problem
The student needs to score at least 65% of the total aggregate marks to pass. The student scored 684 marks but failed by 8% of the total aggregate marks.

### Step 2: Define the variables
Let the maximum aggregate marks be denoted by \( M \).

### Step 3: Calculate the passing marks
To pass, the student needs to score at least 65% of \( M \):
\[ \text{Passing Marks} = 0.65 \times M \]

### Step 4: Determine the marks needed to pass
Since the student failed by 8%, it means the student scored 8% less than the passing marks. Therefore, the marks the student actually needed to pass can be expressed as:
\[ \text{Marks needed to pass} = \text{Marks scored} + \text{Marks failed by} \]
Given that the student scored 684 marks and failed by 8% of \( M \):
\[ \text{Marks needed to pass} = 684 + 0.08M \]

### Step 5: Set up the equation
Now, we can set the two expressions for the marks needed to pass equal to each other:
\[ 0.65M = 684 + 0.08M \]

### Step 6: Solve for \( M \)
To isolate \( M \), we can rearrange the equation:
\[ 0.65M - 0.08M = 684 \]
\[ 0.57M = 684 \]
Now, divide both sides by 0.57:
\[ M = \frac{684}{0.57} \]
Calculating this gives:
\[ M = 1200 \]

### Conclusion
The maximum aggregate marks a student can get is \( 1200 \).

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