A Student secures 50% and failed by 20 marks. If he scores 60% he would pass by 25 more marks. Find the maximum marks of the examination?

Let's denote the maximum marks of the examination by \( x \).

### Step 1: Understanding the Problem
- The student secures 50% of the maximum marks and fails by 20 marks.
- If the student had scored 60%, they would have passed by 25 marks.

### Step 2: Set Up Equations
- The marks obtained when the student scores 50% are \( 0.5x \).
- The passing marks are \( 0.5x + 20 \) because the student fails by 20 marks.

When the student scores 60%, the marks obtained are \( 0.6x \).
- The passing marks are also \( 0.6x - 25 \) because the student passes by 25 marks.

Since the passing marks are the same in both cases, we can set up the equation:

\[
0.5x + 20 = 0.6x - 25
\]

### Step 3: Solve the Equation
Let's solve this equation for \( x \).

\[
0.6x - 0.5x = 20 + 25
\]

\[
0.1x = 45
\]

\[
x = \frac{45}{0.1} = 450
\]

So, the maximum marks of the examination are **450**.

Would you like more details or have any questions? Here are some related questions:

1. How many marks did the student obtain with 50%?
2. What is the passing percentage for this exam?
3. If the student scored 55%, how many marks would they need to pass?
4. What would be the new passing marks if the student had to pass by 10 marks at 60%?
5. How much would the student need to score to just pass the exam?

**Tip:** When dealing with percentage problems, it’s helpful to translate word problems into equations to systematically solve for the unknown variable.

Learn how to calculate the maximum marks of an examination using a percentage problem. This problem involves setting up and solving equations based on percentage scores and passing marks. Suitable for high school students.

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