Let's solve this step by step:

1. Let the total marks be $T$.

2. The student scored 45% of the total marks, so the marks obtained by the student can be expressed as: $\text{Marks obtained} = 0.45T$

3. The student failed by 15 marks, meaning the student scored 15 marks less than the passing marks. Therefore: $0.45T = 150 - 15$

4. Simplify the equation: $0.45T = 135$

5. Solve for $T$: $T = \frac{135}{0.45} = 300$

So, the total marks for the exam were 300.

Would you like further details or do you have any additional questions?

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Here are some related questions:

1. If a student scores 60% in the same exam, how many marks would they obtain?
2. What is the minimum percentage needed to pass if the total marks are 400?
3. How many marks above the passing score would a student who scored 75% obtain?
4. What percentage of the total marks is needed to score exactly 180 marks?
5. If another student scored 90% in the exam, what would their score be?
6. How many more marks would a student need to pass if they scored 120 marks?
7. If the passing percentage were increased to 55%, what would the new passing marks be?
8. What would be the difference in marks between a student scoring 85% and another scoring 50%?

Tip: Always check the relationship between percentages, actual marks, and total marks to solve problems involving exam scores effectively.