If a student scores 15 marks out of 80, what percentage of the total marks has the student obtained?

Introduction / Context:
Percent questions like this are very common in school exams and aptitude tests. Here we are asked to convert a score of 15 marks out of a maximum of 80 marks into a percentage. Understanding how to convert a fraction or ratio into a percentage is a basic but very important skill, because exam scores, discounts, profit and loss, and many real life comparisons are often expressed in percent form.

Given Data / Assumptions:

Total marks in the test = 80.
Marks obtained by the student = 15.
We need to find what percent 15 is of 80.
We assume a simple percentage calculation with no negative marking or weighting.

Concept / Approach:
To convert a part of a whole into a percentage, we use the standard formula:
percentage = (part / whole) * 100 Here, the part is the marks obtained and the whole is the maximum possible marks. After computing the fraction, we multiply by 100 to convert it into percent form. This method works for marks, money, quantities and any other similar comparison situations.

Step-by-Step Solution:
Step 1: Identify the part and the whole. Part = 15, whole = 80. Step 2: Write the basic fraction as 15 / 80. Step 3: Convert to percent using the formula (15 / 80) * 100. Step 4: Simplify 15 / 80. Divide numerator and denominator by 5 to get 3 / 16. Step 5: Now calculate (3 / 16) * 100. First compute 100 / 16 = 6.25. Step 6: Multiply 3 * 6.25 = 18.75. Step 7: Therefore the required percentage is 18.75%.

Verification / Alternative check:
Another way is to convert 18.75% back into marks and see if we get 15. Compute 18.75% of 80 as (18.75 / 100) * 80. First calculate 80 / 100 = 0.8. Then 18.75 * 0.8 = 15. This matches the original marks, so our percentage is consistent and correctly calculated.

Why Other Options Are Wrong:
12.5% corresponds to 0.125 * 80 = 10 marks, which is less than 15.
16.5% corresponds to 0.165 * 80 = 13.2 marks, still not equal to 15.
20% corresponds to 0.20 * 80 = 16 marks, slightly more than 15.
25% corresponds to 0.25 * 80 = 20 marks, which is much higher than the obtained score.

Common Pitfalls:
A common mistake is to divide 80 by 15 instead of 15 by 80, which reverses the ratio and gives a completely wrong answer. Another error is forgetting to multiply by 100 at the end, which leaves the result as a decimal fraction rather than a percentage. Careless rounding too early in the calculation can also cause small errors, so it is better to simplify fractions exactly when possible and only round at the final step if required.

Final Answer:
The student obtained 18.75% of the total marks.