Calculating Maximum Marks from Percentage Score

This problem asks us to find the total possible marks in an examination, given the percentage score obtained by a student and the actual marks corresponding to that percentage.

We are told that Ravi scored 72% marks, and this score is equal to 360 marks. We need to determine the maximum possible marks for the examination.

Let's denote the maximum marks of the examination as \(M\).

According to the problem statement, 72% of the maximum marks \(M\) is equal to 360 marks. We can write this relationship as an equation:

72% of \(M\) = 360

To solve for \(M\), we first need to convert the percentage into a decimal or a fraction. 72% can be written as \(\frac{72}{100}\) or 0.72.

Using the decimal form, the equation becomes:

\(0.72 \times M = 360\)

To isolate \(M\), we need to divide both sides of the equation by 0.72:

\(M = \frac{360}{0.72}\)

Alternatively, using the fraction form:

\(\frac{72}{100} \times M = 360\)

\(M = 360 \times \frac{100}{72}\)

Let's perform the calculation:

\(M = \frac{36000}{72}\)

We can simplify this fraction or perform the division directly.

Dividing 36000 by 72:

\(\frac{360}{72} = 5\)

So, \(\frac{36000}{72} = \frac{360 \times 100}{72} = 5 \times 100 = 500\)

Thus, the maximum marks for the examination are 500.

Let's verify the answer: 72% of 500 = \(\frac{72}{100} \times 500 = 72 \times 5 = 360\). This matches the given information.

The steps are:

1. Understand the relationship: Percentage score is (Obtained Marks / Maximum Marks) * 100.
2. Set up an equation based on the given information.
3. Convert the percentage to a decimal or fraction.
4. Solve the equation for the unknown maximum marks.

Let's represent the information in a table format:

The equation formed is \(72\% \times M = 360\).

Solving for \(M\):

\(M = \frac{360}{72\%} = \frac{360}{\frac{72}{100}} = 360 \times \frac{100}{72} = \frac{36000}{72} = 500\)

Therefore, the maximum marks are 500.

Revision Table: Percentage Calculation Basics

Additional Information: Understanding Marks and Percentages

In examinations, marks represent the points obtained by a student. The maximum marks are the total possible points one could score in that exam. A percentage score is a way to express the obtained marks as a fraction of the maximum marks, scaled to 100.

The relationship is key:

• Percentage Score = \(\left(\frac{\text{Obtained Marks}}{\text{Maximum Marks}}\right) \times 100\)

We used this relationship in reverse to find the maximum marks when the percentage and obtained marks were known. Problems involving percentages in exams are common and understanding this basic formula is crucial.