In an examination, students were required to obtain 36% pass marks. A student obtained 83 marks but failed by 7 marks. Calculate the maximum marks allotted for the examination.

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Points to Remember:

  • This is a mathematical word problem requiring calculation.
  • Keywords: pass marks, obtained marks, failed by, maximum marks.
  • The approach is purely factual and mathematical.

Introduction:

This question tests the ability to solve a simple mathematical word problem involving percentages. The problem presents a scenario where a student’s performance is evaluated against a minimum pass percentage. We need to determine the total marks allotted for the examination based on the given information. The core concept involves understanding the relationship between the percentage of marks obtained, the marks obtained, the pass percentage, and the total marks.

Body:

Understanding the Problem:

The student obtained 83 marks but failed by 7 marks. This means that the pass mark was 83 + 7 = 90 marks.

Calculating Maximum Marks:

The pass mark represents 36% of the maximum marks. We can set up an equation to solve for the maximum marks (let’s denote maximum marks as ‘x’):

36% of x = 90

This can be written as:

(36/100) * x = 90

To solve for x, we can multiply both sides by 100/36:

x = 90 * (100/36)

x = 9000/36

x = 250

Therefore, the maximum marks allotted for the examination were 250.

Verification:

36% of 250 = (36/100) * 250 = 90. This confirms that the pass mark was indeed 90. The student obtained 83 marks, failing by 7 marks (90 – 83 = 7), as stated in the problem.

Conclusion:

In summary, by understanding the relationship between the pass percentage, the pass mark, and the marks obtained by the student, we were able to calculate the maximum marks for the examination. The maximum marks allotted for the examination were 250. This problem highlights the importance of careful reading and the application of basic percentage calculations in solving real-world problems. This simple mathematical exercise demonstrates the practical application of percentages in educational assessments and emphasizes the need for clear and accurate calculation in determining student performance. The solution underscores the importance of precise mathematical reasoning in various contexts.

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