Puneet scored 10% marks in an exam and failed by 50 marks. If he scored 40% marks, then he gets 25 marks more than passing marks. What is the passing marks for the exam?

Options

A. 25
B. 200
C. 150
D. 75

Answer

To find the passing marks for the exam, we can follow these steps:

### Step 1: Let the total marks be X.
We start by defining the total marks of the exam as \( X \).

### Step 2: Determine the passing marks based on Puneet's score.
Puneet scored 10% of the total marks and failed by 50 marks. This can be expressed mathematically as:
\[ \text{Passing Marks} = 10\% \text{ of } X + 50 \]
This can be written as:
\[ \text{Passing Marks} = 0.1X + 50 \]

### Step 3: Analyze the second condition.
If Puneet scored 40% of the total marks, he would have scored 25 marks more than the passing marks. This can be expressed as:
\[ 0.4X = \text{Passing Marks} + 25 \]

### Step 4: Substitute the expression for passing marks into the equation.
Now, we can substitute the expression for passing marks from Step 2 into the equation from Step 3:
\[ 0.4X = (0.1X + 50) + 25 \]
This simplifies to:
\[ 0.4X = 0.1X + 75 \]

### Step 5: Solve for X.
Now, we will isolate \( X \):
\[ 0.4X - 0.1X = 75 \]
\[ 0.3X = 75 \]
\[ X = \frac{75}{0.3} = 250 \]

### Step 6: Calculate the passing marks.
Now that we have the total marks \( X = 250 \), we can find the passing marks using the expression from Step 2:
\[ \text{Passing Marks} = 0.1(250) + 50 = 25 + 50 = 75 \]

### Conclusion
The passing marks for the exam are **75**.

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