In an examination , one requires 40 % marks to pass , Vivek gets 185 marks and fails by 15 marks . What are the maximum marks ?

Options

A. 500
B. 400
C. 300
D. 600

Answer

To solve the problem step by step, we will follow the information given in the question.

### Step 1: Understand the problem
We know that Vivek needs to score at least 40% of the maximum marks to pass the examination. He scored 185 marks but failed by 15 marks. This means if he had scored 15 more marks, he would have passed.

### Step 2: Determine the passing marks
Since Vivek fails by 15 marks, we can find the passing marks by adding 15 to the marks he scored:
\[ \text{Passing Marks} = \text{Vivek's Marks} + 15 = 185 + 15 = 200 \]

### Step 3: Set up the equation for maximum marks
Let the maximum marks be represented by \( x \). According to the problem, to pass, Vivek needs to score at least 40% of the maximum marks:
\[ \text{Passing Marks} = 40\% \text{ of } x \]
This can be expressed mathematically as:
\[ 200 = \frac{40}{100} \times x \]

### Step 4: Solve for maximum marks
To find \( x \), we can rearrange the equation:
\[ 200 = \frac{2}{5} \times x \]
Now, multiply both sides by \( \frac{5}{2} \) to isolate \( x \):
\[ x = 200 \times \frac{5}{2} = 200 \times 2.5 = 500 \]

### Conclusion
The maximum marks for the examination are \( 500 \).