Introduction:
In this question, we are given that the passing marks in an examination are 36%. We are also given that a student scores 72 marks but fails by 18 marks. We need to determine the maximum marks of the examination.

Given:
- The passing marks in the examination are 36%.
- The student scores 72 marks but fails by 18 marks.

Approach:
To find the maximum marks of the examination, we need to first determine the passing marks. Once we have the passing marks, we can use them to calculate the maximum marks.

Step 1: Calculate the Passing Marks:
To calculate the passing marks, we will use the given passing percentage. The passing percentage is 36%. We can calculate the passing marks using the following formula:

Passing Marks = (Passing Percentage / 100) * Maximum Marks

Let's substitute the values:
Passing Marks = (36/100) * Maximum Marks

Step 2: Calculate the Maximum Marks:
We are given that the student scores 72 marks but fails by 18 marks. This means that the student's marks are 18 marks less than the passing marks.

Passing Marks - Student's Marks = 18
(36/100) * Maximum Marks - 72 = 18

Now, we can solve this equation to find the value of Maximum Marks.

Solution:
Let's solve the equation to find the value of Maximum Marks.

(36/100) * Maximum Marks - 72 = 18

(36/100) * Maximum Marks = 18 + 72
(36/100) * Maximum Marks = 90

Maximum Marks = (90 * 100) / 36
Maximum Marks = 250

Therefore, the maximum marks of the examination are 250.

250