In an examination it is required to get 270 of the aggregate marks to pass. A student gets 216 marks and is declared failed by 8% marks. What are the maximum aggregate marks a student can get ?

Options

A. 825
B. 675
C. 750
D. cannot be determined

Answer

To solve the problem step by step, we need to find the maximum aggregate marks a student can get based on the information provided.

### Step 1: Understand the problem
The student needs to score 270 marks to pass. The student scored 216 marks and failed by 8% of the maximum marks.

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

### Step 3: Calculate the failing marks
Since the student failed by 8% of the maximum marks, we can express this mathematically:
\[ \text{Failing Marks} = 8\% \text{ of } x = \frac{8}{100} \times x = \frac{2}{25} x \]

### Step 4: Set up the equation
If the student had scored 8% more than their actual score, they would have passed. Therefore, we can set up the equation:
\[ 216 + \frac{2}{25} x = 270 \]

### Step 5: Solve the equation
Now, we will solve for \( x \):
1. Rearranging the equation gives:
\[ \frac{2}{25} x = 270 - 216 \]
\[ \frac{2}{25} x = 54 \]

2. To eliminate the fraction, multiply both sides by \( 25 \):
\[ 2x = 54 \times 25 \]

3. Calculate \( 54 \times 25 \):
\[ 54 \times 25 = 1350 \]
Thus, we have:
\[ 2x = 1350 \]

4. Divide both sides by 2 to find \( x \):
\[ x = \frac{1350}{2} = 675 \]

### Conclusion
The maximum aggregate marks a student can get is \( 675 \).