Sanjay scored `56%` marks and passed an exam by 10 marks while Rohit scored `48%` marks but failed by 6 marks. What is the pass percentage?

Options

A. A)`51.5%`
B. B)`51.5%`
C. C)`52%`
D. D)`51%`

Answer

To find the pass percentage based on the scores of Sanjay and Rohit, we can follow these steps:

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

### Step 2: Determine Sanjay's Marks
Sanjay scored 56% of the total marks:
\[ \text{Sanjay's Marks} = 0.56T \]
Since he passed the exam by 10 marks, we can express the passing marks \( P \) as:
\[ P = 0.56T - 10 \]

### Step 3: Determine Rohit's Marks
Rohit scored 48% of the total marks:
\[ \text{Rohit's Marks} = 0.48T \]
Since he failed by 6 marks, we can express the passing marks \( P \) as:
\[ P = 0.48T + 6 \]

### Step 4: Set the Equations Equal
Since both expressions for passing marks \( P \) are equal, we can set them equal to each other:
\[ 0.56T - 10 = 0.48T + 6 \]

### Step 5: Solve for \( T \)
Rearranging the equation gives:
\[ 0.56T - 0.48T = 6 + 10 \]
\[ 0.08T = 16 \]
Now, divide both sides by 0.08:
\[ T = \frac{16}{0.08} = 200 \]

### Step 6: Calculate Passing Marks
Now that we have \( T \), we can find the passing marks using either equation. Using Sanjay's equation:
\[ P = 0.56 \times 200 - 10 = 112 - 10 = 102 \]

### Step 7: Calculate the Pass Percentage
Now, we can calculate the pass percentage:
\[ \text{Pass Percentage} = \left( \frac{P}{T} \right) \times 100 = \left( \frac{102}{200} \right) \times 100 = 51\% \]

### Final Answer
The pass percentage is **51%**.

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