A student scored 45% in an exam and failed by 15 marks. If the passing marks are 150, what were the total marks for the exam?

Let's denote the total marks for the exam as \( T \).

The student scored 45% of the total marks, which can be expressed as:

\[
\text{Marks obtained by the student} = 0.45T
\]

It is given that the student failed by 15 marks, which means that the marks obtained by the student were 15 marks less than the passing marks of 150. Therefore, we can write:

\[
0.45T = 150 - 15
\]

Simplifying the equation:

\[
0.45T = 135
\]

Now, solving for \( T \):

\[
T = \frac{135}{0.45} = 300
\]

So, the total marks for the exam were **300**.

Would you like any further details or have any other questions?

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Here are some related questions:

1. If a student scored 60% in the same exam, how many marks did they obtain?
2. What percentage would a student need to pass if the total marks were 400?
3. If another student scored 75% in this exam, how many marks did they score above the passing mark?
4. What is the minimum percentage required to pass the exam?
5. If the exam were out of 500 marks, what would be the new passing mark if the percentage required to pass remains the same?
6. How many marks would a student lose if they scored 10% less than the passing percentage?
7. What would be the difference in marks between a student who scored 85% and the student who scored 45%?
8. How many marks would a student score if they obtained 90% in the exam?

**Tip:** When dealing with percentage problems, it's often useful to express all values in terms of the unknown variable before solving for it.

Learn how to calculate the total marks for an exam based on a student's score and the passing criteria. This problem involves using percentages and equations to determine the total marks when the passing marks and student's score are known. Suitable for high school students studying percentage calculations and algebraic equations.

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