In an examination, a student requires 40% of the total marks to pass. If the student secures 185 marks and fails by 15 marks, find the total marks.

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the problem
The student needs 40% of the total marks to pass the examination. The student scored 185 marks but failed by 15 marks.

### Step 2: Calculate the passing marks
Since the student failed by 15 marks, we can find the passing marks by adding the marks the student scored to the marks he failed by.

\[ \text{Passing Marks} = \text{Marks Secured} + \text{Marks Failed By} \]
\[ \text{Passing Marks} = 185 + 15 = 200 \]

### Step 3: Set up the equation for total marks
We know that the passing marks (200) is equal to 40% of the total marks (let's denote total marks as \( T \)). We can write this as an equation:

\[ 200 = 40\% \text{ of } T \]
\[ 200 = \frac{40}{100} \times T \]

### Step 4: Solve for total marks
To find \( T \), we can rearrange the equation:

\[ 200 = \frac{40}{100} \times T \]
\[ 200 = \frac{2}{5} \times T \]

Now, to isolate \( T \), we can multiply both sides by \( \frac{5}{2} \):

\[ T = 200 \times \frac{5}{2} \]
\[ T = 200 \times 2.5 \]
\[ T = 500 \]

### Conclusion
The total marks for the examination is \( 500 \).

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