In an examination a candidate scored 30% of the total marks and failed by 30 marks. If the pass mark is 60% of the total marks, what is the maximum possible total mark for the examination?

Introduction / Context:
This examination style problem involves interpreting percentages of total marks and understanding how many marks a candidate falls short by. With a known failure margin in marks and two given percentage levels, you can work backwards to determine the total marks in the exam. This pattern is very popular in competitive tests for building comfort with percentages and algebraic reasoning.

Given Data / Assumptions:

The candidate scored 30% of the maximum marks.

The candidate failed and was 30 marks short of the pass mark.

The pass mark is 60% of the total marks.

We need to find the maximum total marks in the examination.

Concept / Approach:
Let the maximum marks be M. Then the candidate mark is 30% of M, and the passing mark is 60% of M. The difference between these two is given as 30 marks. In symbols:
60% of M − 30% of M = 30.
Use percent to decimal conversion and solve the resulting linear equation to get M. This is a direct application of basic algebra combined with percentage calculations.

Step-by-Step Solution:
Step 1: Let maximum marks be M.Step 2: Candidate marks = 30% of M = (30 / 100) * M = 0.30 * M.Step 3: Pass marks = 60% of M = (60 / 100) * M = 0.60 * M.Step 4: Given that the candidate failed by 30 marks, so 0.60 * M − 0.30 * M = 30.Step 5: Left side simplifies to (0.60 − 0.30) * M = 0.30 * M.Step 6: Therefore 0.30 * M = 30.Step 7: Solve for M: M = 30 / 0.30 = 30 * (100 / 30) = 100.

Verification / Alternative check:
If maximum marks are 100, then candidate marks = 30% of 100 = 30. Pass marks = 60% of 100 = 60. The difference between pass marks and candidate marks is 60 − 30 = 30 marks, exactly as stated in the question. Hence the total marks of 100 are fully consistent.

Why Other Options Are Wrong:
If M were 300, then 30% of 300 = 90 and 60% of 300 = 180, difference 90 marks, not 30.
For 450 or 600, the differences between 30% and 60% would be very large (135 and 180 respectively), again not 30.
750 would give an even larger difference. None of these values satisfy the equation 0.30 * M = 30.

Common Pitfalls:
Some students confuse the meaning of failing by 30 marks and incorrectly treat 30 as a percentage instead of a number of marks. Others mix up which percentage corresponds to pass and which to the candidate score. A clear variable definition, consistent use of the percentage formula, and careful reading of the phrase "failed by 30 marks" are crucial for solving this type of question correctly.

Final Answer:
The maximum total marks in the examination are 100.