A person scores `45%` of the total mark 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, we will use the information given in the question regarding the percentages and the marks.

### Step 1: Define the maximum marks
Let the maximum marks of the exam be denoted as \( X \).

### Step 2: Calculate the marks scored by the person
The person scores \( 45\% \) of the total marks. Therefore, the marks scored by the person can be calculated as:
\[ \text{Marks scored} = 45\% \text{ of } X = \frac{45}{100} \times X = \frac{45X}{100} \]

### Step 3: Calculate the passing marks
The passing percentage is \( 55\% \). Thus, the minimum marks required to pass the exam is:
\[ \text{Passing marks} = 55\% \text{ of } X = \frac{55}{100} \times X = \frac{55X}{100} \]

### Step 4: Set up the equation based on the information given
According to the question, the person fails by \( 40 \) marks. This means that the difference between the passing marks and the marks scored is \( 40 \):
\[ \text{Passing marks} - \text{Marks scored} = 40 \]
Substituting the values we calculated:
\[ \frac{55X}{100} - \frac{45X}{100} = 40 \]

### Step 5: Simplify the equation
Now, simplify the left side of the equation:
\[ \frac{55X - 45X}{100} = 40 \]
\[ \frac{10X}{100} = 40 \]

### Step 6: Solve for \( X \)
To eliminate the fraction, multiply both sides by \( 100 \):
\[ 10X = 4000 \]
Now, divide both sides by \( 10 \):
\[ X = 400 \]

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

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