Calculating Maximum Examination Marks

This problem requires us to find the total maximum marks of an examination given the passing percentage, the marks a student obtained, and the number of marks by which the student failed.

Understanding the Given Information

• Passing percentage required: 33% of the total marks
• Marks obtained by the student: 148 marks
• Marks by which the student failed: 50 marks

The key insight here is that if the student had obtained 50 more marks, they would have passed the examination. Therefore, the passing marks can be calculated by adding the marks obtained and the marks failed by.

Calculating the Passing Marks

The number of marks required to pass the examination is the sum of the marks the student got and the marks they needed to pass.

Passing Marks $=$ Marks Obtained $+$ Marks Failed By

Passing Marks $=$ $148 + 50$

Passing Marks $=$ $198$ marks

So, the minimum marks required to pass the examination are 198.

Relating Passing Marks to Total Marks Percentage

We are told that the passing marks are 33% of the total marks. Let's denote the maximum marks (total marks) of the examination as $M$.

According to the problem statement:

33% of Total Marks $=$ Passing Marks

$33\%$ of $M = 198$

We can write 33% as a fraction or a decimal:

$\frac{33}{100} \times M = 198$

Solving for the Maximum Marks ($M$)

Now we need to isolate $M$ in the equation:

$\frac{33}{100} \times M = 198$

To find $M$, we can multiply both sides of the equation by $\frac{100}{33}$:

$M = 198 \times \frac{100}{33}$

We can simplify the calculation by dividing 198 by 33. Let's perform the division:

$198 \div 33$

$33 \times 6 = 198$

So, $198/33 = 6$.

Now substitute this back into the equation for $M$:

$M = 6 \times 100$

$M = 600$

Therefore, the maximum marks for the examination are 600.

Verification

Let's check if 33% of 600 is indeed 198.

$33\%$ of $600 = \frac{33}{100} \times 600 = 33 \times 6 = 198$

The passing marks are 198. The student got 148 marks, which is $198 - 148 = 50$ marks less than the passing marks. This matches the information given that the student failed by 50 marks.

The calculations are consistent with the problem statement.

The maximum marks of the examination are 600.

Revision Table: Examination Marks Calculation

Additional Information: Percentage Concepts

Understanding percentages is crucial for solving many quantitative problems, including those related to examination marks.

• What is a Percentage? A percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol '%'. For example, 33% means 33 out of 100, or $\frac{33}{100}$.
• Calculating Percentage of a Quantity: To find a percentage of a quantity, convert the percentage to a decimal or fraction and multiply by the quantity. For example, 33% of 600 is $\frac{33}{100} \times 600$.
• Finding the Whole from a Percentage: If you know that a certain number is a specific percentage of a whole, you can find the whole by dividing the number by the percentage (in decimal or fractional form). For example, if 198 is 33% of $M$, then $M = \frac{198}{33\%} = \frac{198}{0.33} = \frac{198}{33/100} = 198 \times \frac{100}{33}$.

These basic percentage calculations are fundamental in various arithmetic and quantitative aptitude problems.