A student has to score 60% to pass exam. He scores 225 marks & failed by 15%. Find the maximum marks of exam.

Options

A. 400
B. 500
C. 600
D. Can't be determined

Answer

To solve the problem step by step, we can break it down as follows:

### Step 1: Understand the Passing Criteria
The student needs to score 60% to pass the exam.

### Step 2: Determine the Marks Required to Pass
Let the maximum marks of the exam be denoted as \( M \). The passing marks, which is 60% of the maximum marks, can be calculated as:
\[ \text{Passing Marks} = 0.6 \times M \]

### Step 3: Determine the Marks the Student Needs to Pass
The student scored 225 marks but failed by 15%. This means that the student needed 15% more than what he scored to pass. Therefore, we can express the required marks to pass as:
\[ \text{Required Marks to Pass} = 225 + 0.15 \times M \]

### Step 4: Set Up the Equation
Since the required marks to pass is equal to the passing marks, we can set up the equation:
\[ 0.6 \times M = 225 + 0.15 \times M \]

### Step 5: Solve the Equation
Now, we can solve for \( M \):
1. Rearranging the equation gives:
\[ 0.6M - 0.15M = 225 \]
2. Simplifying the left side:
\[ 0.45M = 225 \]
3. Dividing both sides by 0.45:
\[ M = \frac{225}{0.45} \]
4. Calculating \( M \):
\[ M = 500 \]

### Conclusion
The maximum marks of the exam are \( \boxed{500} \).

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