A scores 10% and fails by 30 marks.B scores 40% marks and gets 30 marks more than the minimum marks needed to pass the exam. What are the maximum marks for the exam?

Let's solve this step by step:

1. According to the problem, A scores 10% of the total marks and still fails by 30 marks. This means the passing mark is 10% of total marks + 30.

2. Similarly, B scores 40% of the total marks which is 30 marks more than the passing mark. This means the passing mark is 40% of total marks - 30.

3. From the above two points, we can create the following equation: 10% of total marks + 30 = 40% of total marks - 30.

4. Let's denote the total marks as 'x'. So the equation becomes: 0.10x + 30 = 0.40x - 30.

5. Solving this equation for 'x' gives us the total marks. First, let's get rid of the decimal by multiplying the entire equation by 10: x + 300 = 4x - 300.

6. Now, let's bring the terms involving 'x' to one side and the constants to the other side: 4x - x = 300 + 300.

7. This simplifies to: 3x = 600.

8. Finally, solving for 'x' gives: x = 600 / 3 = 200.

So, the maximum marks for the exam are 200.