A candidate who gets `30%` marks in an examination fails by 45 marks but another candidate who gets `40%` marks gets 30 marks more than the passing mark, Then find the percentage of pass marks out of total marks.

Options

A. `42%`
B. `32%`
C. `38%`
D. `36%`

Answer

To solve the problem step by step, we will define the variables and set up equations based on the information provided in the question.

### Step 1: Define the total marks
Let the total marks of the examination be denoted by \( X \).

### Step 2: Set up the equation for the first candidate
The first candidate scores \( 30\% \) of the total marks and fails by \( 45 \) marks. Therefore, the passing marks can be expressed as:
\[ \text{Passing Marks} = 30\% \text{ of } X + 45 \]
This can be written mathematically as:
\[ \text{Passing Marks} = 0.3X + 45 \]

### Step 3: Set up the equation for the second candidate
The second candidate scores \( 40\% \) of the total marks and gets \( 30 \) marks more than the passing marks. Thus, we can express this as:
\[ \text{Passing Marks} = 40\% \text{ of } X - 30 \]
This can be written mathematically as:
\[ \text{Passing Marks} = 0.4X - 30 \]

### Step 4: Equate the two expressions for passing marks
Since both expressions represent the passing marks, we can set them equal to each other:
\[ 0.3X + 45 = 0.4X - 30 \]

### Step 5: Solve for \( X \)
To solve for \( X \), we will rearrange the equation:
1. Move \( 0.3X \) to the right side:
\[ 45 + 30 = 0.4X - 0.3X \]
This simplifies to:
\[ 75 = 0.1X \]
2. Now, divide both sides by \( 0.1 \):
\[ X = \frac{75}{0.1} = 750 \]

### Step 6: Calculate the passing marks
Now that we have the total marks \( X = 750 \), we can calculate the passing marks using either of the expressions. We will use the first candidate's expression:
\[ \text{Passing Marks} = 0.3 \times 750 + 45 \]
Calculating this gives:
\[ \text{Passing Marks} = 225 + 45 = 270 \]

### Step 7: Find the percentage of passing marks
To find the percentage of passing marks out of the total marks, we use the formula:
\[ \text{Percentage of Passing Marks} = \left( \frac{\text{Passing Marks}}{X} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage of Passing Marks} = \left( \frac{270}{750} \right) \times 100 \]
Calculating this gives:
\[ \text{Percentage of Passing Marks} = 36\% \]

### Final Answer
The percentage of pass marks out of total marks is **36%**.