Ram scored 40% marks and failed by 20 marks. Aditya scored 45% marks and obtained 30 marks more than those of required to pass. The pass percentage is ?

Options

A. `33%`
B. `43%`
C. `38%`
D. `42%`

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define Variables
Let the total marks be represented as \( X \).

### Step 2: Set Up Equations Based on Given Information
1. **For Ram**:
- Ram scored 40% of the total marks and failed by 20 marks.
- This can be expressed as:
\[ 0.4X + 20 = \text{Passing Marks} \]

2. **For Aditya**:
- Aditya scored 45% of the total marks and obtained 30 marks more than required to pass.
- This can be expressed as:
\[ 0.45X - 30 = \text{Passing Marks} \]

### Step 3: Set the Two Equations Equal to Each Other
Since both expressions equal the passing marks, we can set them equal to each other:
\[ 0.4X + 20 = 0.45X - 30 \]

### Step 4: Solve for \( X \)
Rearranging the equation:
\[ 0.4X + 20 + 30 = 0.45X \]
\[ 0.4X + 50 = 0.45X \]
Subtract \( 0.4X \) from both sides:
\[ 50 = 0.45X - 0.4X \]
\[ 50 = 0.05X \]
Now, divide both sides by \( 0.05 \):
\[ X = \frac{50}{0.05} = 1000 \]

### Step 5: Find the Passing Marks
Now that we have \( X \), we can find the passing marks using Ram's equation:
\[ \text{Passing Marks} = 0.4 \times 1000 + 20 \]
\[ \text{Passing Marks} = 400 + 20 = 420 \]

### Step 6: Calculate the Passing Percentage
To find the passing percentage, we use the formula:
\[ \text{Passing Percentage} = \left(\frac{\text{Passing Marks}}{\text{Total Marks}}\right) \times 100 \]
Substituting the values:
\[ \text{Passing Percentage} = \left(\frac{420}{1000}\right) \times 100 = 42\% \]

### Final Answer
The pass percentage is **42%**.

---