A student must secure 40 percent marks to pass. He scores 67 marks and fails by 13 marks. What are the maximum marks for the examination?

Introduction / Context:
This question links pass percentage, marks obtained and shortfall in marks to the total maximum marks of an examination. It is frequently seen in recruitment and academic entrance test papers.

Given Data / Assumptions:

• Passing marks = 40 percent of maximum marks.
• The student scores 67 marks.
• He fails by 13 marks.
• We need to find the maximum marks.

Concept / Approach:
If the student fails by 13 marks, then passing marks equal his marks plus 13. Since passing marks are 40 percent of the maximum, we can express 40 percent of the total as that number and solve for the maximum marks using a simple linear equation.

Step-by-Step Solution:
Let maximum marks be M.Passing marks = 40 percent of M = 0.40 * M.He scores 67 and fails by 13, hence passing marks = 67 + 13 = 80.So 0.40 * M = 80.Therefore M = 80 / 0.40 = 80 * (10 / 4) = 80 * 2.5 = 200.

Verification / Alternative check:
Check: 40 percent of 200 = 0.40 * 200 = 80. The student has 67 marks, which is 13 marks less than 80, so he fails by 13 marks. This confirms that the maximum marks are 200.

Why Other Options Are Wrong:
For maximum marks 300, 40 percent would be 120, which is not 13 more than 67. Similarly, 150 gives passing marks 60, which is less than the student's marks, meaning he would have passed, contradicting the question. The figure 240 leads to 96 passing marks, which does not fit the given shortfall of 13.

Common Pitfalls:
Some students incorrectly treat 67 as 40 percent of total marks and then add 13, which leads to an incorrect equation. Always connect the shortfall with the passing marks, not with the maximum marks directly.

Final Answer:
The maximum marks for the examination are 200.