A student has to secure `35%` marks to pass in a subject. If he gets `82` and fails by 23 marks. What is the maximum mark of the subject ?

Options

A. `300`
B. `250`
C. `350`
D. `400`

Answer

To find the maximum marks of the subject, we can follow these steps:

### Step 1: Determine the passing marks
The student scored 82 marks and failed by 23 marks. Therefore, the passing marks can be calculated as:
\[ \text{Passing Marks} = \text{Marks Obtained} + \text{Marks Needed to Pass} \]
\[ \text{Passing Marks} = 82 + 23 = 105 \]

### Step 2: Set up the equation for maximum marks
We know that the passing marks (105) represent 35% of the total maximum marks (let's denote it as \( X \)). We can express this relationship mathematically as:
\[ 0.35X = 105 \]

### Step 3: Solve for \( X \)
To find \( X \), we can rearrange the equation:
\[ X = \frac{105}{0.35} \]

### Step 4: Calculate \( X \)
Now, we can perform the division:
\[ X = \frac{105}{0.35} = 105 \times \frac{100}{35} \]
\[ X = 105 \times \frac{20}{7} \]
Calculating this gives:
\[ X = 300 \]

### Conclusion
Thus, the maximum marks of the subject are:
\[ \text{Maximum Marks} = 300 \]

---