A person scores 45% of the total marks in the exam and still fails by 40 marks. The passing percentage of the exam is 55%. What is the maximum marks of the exam?

Options

A. 300
B. 350
C. 400
D. 500

Answer

To solve the problem step by step, let's denote the maximum marks of the exam as \( x \).

### Step 1: Understand the given information
- The person scores 45% of the total marks.
- The passing percentage is 55%.
- The person fails by 40 marks.

### Step 2: Set up the equations
From the information given:
- The score of the person is \( 0.45x \) (which is 45% of total marks).
- The passing marks would be \( 0.55x \) (which is 55% of total marks).
- The person fails by 40 marks, which means:
\[ 0.45x + 40 = 0.55x \]

### Step 3: Rearrange the equation
Now, we can rearrange the equation to isolate \( x \):
\[ 0.45x + 40 = 0.55x \]
Subtract \( 0.45x \) from both sides:
\[ 40 = 0.55x - 0.45x \]
This simplifies to:
\[ 40 = 0.10x \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides by 0.10:
\[ x = \frac{40}{0.10} = 400 \]

### Step 5: Conclusion
The maximum marks of the exam are \( 400 \).

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