A student must obtain 33% of the total marks in an examination to pass. The student scored 125 marks and failed by 40 marks. What are the maximum (total) marks for the examination?

Introduction / Context:
This examination problem involves percentages of total marks and the concept of passing marks. The passing mark is a fixed percentage of the total marks. The student has scored a certain number of marks but is short by a known amount. We are asked to find the total marks of the exam. Such questions are standard in quantitative aptitude and help students connect percentage thresholds with absolute scores.

Given Data / Assumptions:
- Passing percentage = 33% of the total marks.- The student scores 125 marks.- The student fails by 40 marks, meaning the student needs 40 more marks to reach the pass mark.- Let the maximum (total) marks of the exam be M.- We must find M.

Concept / Approach:
The pass mark is defined as 33% of the total marks M. Since the student failed by 40 marks, the pass mark is equal to the student's obtained marks plus 40. We therefore set up an equation: 33% of M equals 125 + 40. Solving this linear equation yields the total marks M. This is a straightforward application of percentage and algebra.

Step-by-Step Solution:
Step 1: Let total marks be M.Step 2: Passing marks = 33% of M = (33 / 100) * M.Step 3: The student scored 125 marks and failed by 40 marks.Step 4: Therefore, passing marks = 125 + 40 = 165.Step 5: Set up the equation: (33 / 100) * M = 165.Step 6: Multiply both sides by 100 to eliminate the denominator.33 * M = 165 * 100.Step 7: 165 * 100 = 16,500.Step 8: Now M = 16,500 / 33.Step 9: Divide 16,500 by 33: 33 * 500 = 16,500.Step 10: Hence, M = 500.Therefore, the maximum marks are 500.

Verification / Alternative check:
Check by computing 33% of 500.33% of 500 = (33 / 100) * 500 = 165 marks.The student scored 125 marks and failed by 40 marks.125 + 40 = 165, exactly equal to the required passing marks.This confirms that the total marks are 500.

Why Other Options Are Wrong:
- 600: 33% of 600 = 198, which would require the student to need 198 - 125 = 73 marks more, not 40.- 800: 33% of 800 = 264, implying a shortfall of 139 marks, inconsistent with the given 40 marks.- 1000: 33% of 1,000 = 330, so the student would be short by 205 marks, again incorrect.

Common Pitfalls:
- Misinterpreting "failed by 40 marks" as the student scoring 40 instead of being 40 marks below the passing score.- Using 33% of the obtained marks instead of 33% of the total marks to form the equation.- Arithmetic errors when multiplying or dividing by percentages, such as treating 33% as 0.33 but mis-applying it.- Confusing passing percentage 33% with passing marks 33 directly.

Final Answer:
The maximum marks for the examination are 500.