A student has to score 30% marks to get through. If he gets 30 marks and fails by 30 marks, then find the maximum marks set for the examination.

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the problem
The student needs to score 30% of the maximum marks to pass. He scored 30 marks but failed by 30 marks.

### Step 2: Define the maximum marks
Let the maximum marks be represented by \( x \).

### Step 3: Calculate the passing marks
Since the student needs to score 30% of the maximum marks to pass, the passing marks can be calculated as:
\[ \text{Passing Marks} = 30\% \text{ of } x = \frac{30}{100} \times x = \frac{3}{10} x \]

### Step 4: Determine the actual passing marks
The student scored 30 marks and failed by 30 marks. This means the actual passing marks required are:
\[ \text{Marks scored} + \text{Marks failed by} = 30 + 30 = 60 \]

### Step 5: Set up the equation
Now we can set up the equation based on the passing marks:
\[ \frac{3}{10} x = 60 \]

### Step 6: Solve for \( x \)
To find \( x \), we can multiply both sides of the equation by \( \frac{10}{3} \):
\[ x = 60 \times \frac{10}{3} \]
Calculating this gives:
\[ x = 60 \times \frac{10}{3} = 20 \times 10 = 200 \]

### Step 7: Conclusion
Thus, the maximum marks set for the examination is:
\[ \boxed{200} \]

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