Anurag and Ayush get `48%` & `33%` marks in an exam. If Anurag got 60 marks more than passing marks and Ayush got 15 marks less than passing marks and Veer got `54%` marks, then find Veer got how much more marks than passing marks?

Options

A. 90
B. 55
C. 45
D. 70

Answer

To solve the problem step by step, we will follow the information given about Anurag, Ayush, and Veer.

### Step 1: Set up the equations based on the information given.
Let the total marks of the exam be \( X \).

- Anurag scored \( 48\% \) of \( X \) and got \( 60 \) marks more than the passing marks.
- Ayush scored \( 33\% \) of \( X \) and got \( 15 \) marks less than the passing marks.

Let the passing marks be \( P \).

From Anurag's information, we can write:
\[ 0.48X = P + 60 \]

From Ayush's information, we can write:
\[ 0.33X = P - 15 \]

### Step 2: Set the two equations equal to each other.
Since both equations equal \( P \), we can set them equal to each other:
\[ 0.48X - 60 = 0.33X + 15 \]

### Step 3: Solve for \( X \).
Rearranging the equation:
\[ 0.48X - 0.33X = 15 + 60 \]
\[ 0.15X = 75 \]
Now, divide both sides by \( 0.15 \):
\[ X = \frac{75}{0.15} = 500 \]

### Step 4: Find the passing marks \( P \).
Now that we know \( X \), we can find \( P \) using either of the equations. We will use Anurag's equation:
\[ 0.48(500) = P + 60 \]
Calculating \( 0.48 \times 500 \):
\[ 240 = P + 60 \]
Now, subtract \( 60 \) from both sides:
\[ P = 240 - 60 = 180 \]

### Step 5: Calculate Veer’s marks.
Veer scored \( 54\% \) of \( X \):
\[ 0.54(500) = 270 \]

### Step 6: Find how much more Veer scored than the passing marks.
Now we find how much more Veer scored than the passing marks:
\[ 270 - 180 = 90 \]

### Conclusion:
Veer scored \( 90 \) marks more than the passing marks.

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