A candidate who gets 20% marks in an examination fails by 30 marks but another candidate who gets 32% gets 42 marks more than the pass mark. Then the percentage of pass marks is

Options

A. `52%`
B. `50%`
C. `33%`
D. `25%`

Answer

To solve the problem step by step, we will denote the maximum marks of the examination as \( M \) and the pass marks as \( P \).

### Step 1: Establish equations based on the information given
1. The first candidate scores 20% of the maximum marks and fails by 30 marks:
\[ 0.2M = P - 30 \]

2. The second candidate scores 32% of the maximum marks and exceeds the pass mark by 42 marks:
\[ 0.32M = P + 42 \]

### Step 2: Set up the equations
From the two equations we have:
1. \( P = 0.2M + 30 \) (from the first candidate)
2. \( P = 0.32M - 42 \) (from the second candidate)

### Step 3: Equate the two expressions for \( P \)
Since both expressions equal \( P \), we can set them equal to each other:
\[ 0.2M + 30 = 0.32M - 42 \]

### Step 4: Solve for \( M \)
Rearranging the equation:
\[ 30 + 42 = 0.32M - 0.2M \]
\[ 72 = 0.12M \]
Now, divide both sides by 0.12:
\[ M = \frac{72}{0.12} = 600 \]

### Step 5: Find the pass marks \( P \)
Now that we have \( M \), we can substitute back to find \( P \):
Using the first equation:
\[ P = 0.2 \times 600 + 30 \]
\[ P = 120 + 30 = 150 \]

### Step 6: Calculate the percentage of pass marks
To find the percentage of the pass marks:
\[ \text{Percentage of pass marks} = \left(\frac{P}{M}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage of pass marks} = \left(\frac{150}{600}\right) \times 100 = 25\% \]

### Final Answer
The percentage of pass marks is **25%**.