Pass percentage of an examination is 35%. If a student who get 210 marks, failed by 14 marks, then what are the maximum marks of the examination?
640
Understanding the Examination Pass Criteria
The question provides information about an examination: the pass percentage, the marks obtained by a student, and the margin by which the student failed. We need to use this information to determine the maximum possible marks for the examination.
Calculating the Passing Marks
A student scored 210 marks but failed by 14 marks. This means that to pass the examination, the student needed to score 14 marks more than what they got.
- Student's score = 210 marks
- Marks needed to pass = 14 marks
- Passing marks = Student's score + Marks needed to pass
- Passing marks = \(210 + 14 = 224\) marks
So, the minimum marks required to pass the examination are 224.
Relating Passing Marks to Pass Percentage
The problem states that the pass percentage for the examination is 35%. This means that the passing marks (which we calculated as 224) represent 35% of the total maximum marks for the examination.
Let \(M\) be the maximum marks for the examination.
According to the problem:
\(35\%\) of \(M = \text{Passing Marks}\)
We can write this relationship as an equation:
\(\frac{35}{100} \times M = 224\)
Solving for Maximum Marks
Now, we need to solve this equation for \(M\), the maximum marks.
To isolate \(M\), we can multiply both sides of the equation by \(\frac{100}{35}\):
\(M = 224 \times \frac{100}{35}\)
We can simplify the fraction \(\frac{100}{35}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
\(\frac{100 \div 5}{35 \div 5} = \frac{20}{7}\)
So the equation becomes:
\(M = 224 \times \frac{20}{7}\)
Now, we can divide 224 by 7:
\(224 \div 7 = 32\)
Substitute this back into the equation:
\(M = 32 \times 20\)
\(M = 640\)
Summary of Calculations
| Detail | Value |
|---|---|
| Student's Score | 210 marks |
| Failed By | 14 marks |
| Passing Marks | \(210 + 14 = 224\) marks |
| Pass Percentage | 35% |
| Equation | \(0.35 \times M = 224\) |
| Maximum Marks (\(M\)) | \(\frac{224}{0.35} = 640\) marks |
Therefore, the maximum marks of the examination are 640.
Revision Table: Key Concepts Review
| Concept | Description | Formula/Example |
|---|---|---|
| Percentage | A fraction of 100. Used to express a part of a whole. | \(p\% = \frac{p}{100}\) |
| Calculating Percentage of a Value | To find \(p\%\) of a value \(V\), calculate \(\frac{p}{100} \times V\). | 35% of 640 = \(\frac{35}{100} \times 640\) |
| Finding the Whole from a Percentage | If \(p\%\) of \(M\) is \(V\), then \(M = V \times \frac{100}{p}\). | If 35% of \(M\) is 224, \(M = 224 \times \frac{100}{35}\). |
| Passing Marks | The minimum score required to pass an exam. Calculated from total marks and pass percentage, or from a failing score and the margin of failure. | Student Score + Failed By = Passing Marks |
Additional Information: Percentage Calculations in Exams
Percentage calculations are very common in examination contexts. Understanding how to work with percentages, scores, maximum marks, and pass/fail criteria is crucial for various problems.
- Scores and Percentages: A score is a raw number of marks. A percentage score is the score expressed as a percentage of the maximum marks (\(\frac{\text{Score}}{\text{Maximum Marks}} \times 100\%\)).
- Pass/Fail Criteria: Exams often set a minimum percentage score required to pass (pass percentage). Any score below this percentage results in a failure.
- Calculating Required Marks: If you know the pass percentage and the maximum marks, you can find the required passing marks by calculating the percentage of the maximum marks. Required Marks = Pass Percentage \(\times\) Maximum Marks.
- Calculating Maximum Marks: If you know the passing marks and the pass percentage, you can find the maximum marks using the formula: Maximum Marks = \(\frac{\text{Passing Marks}}{\text{Pass Percentage}} \times 100\).
These basic concepts help in solving various problems related to examination scores and percentages.
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