To determine the maximum marks in the examination, we analyze the provided information: The passing mark is 300. A student scoring 225 failed by 10%. This implies the passing mark is 10% higher than the student's score.
Let \( M \) represent the maximum marks. The passing percentage is calculated as:
\[\frac{300}{M} \times 100\]
The student's obtained percentage is:
\[\frac{225}{M} \times 100\]
As per the problem statement, the student's percentage is 10% less than the passing percentage:
\[\frac{300}{M} \times 100 = \left(\frac{225}{M} \times 100\right) + 10\]
Simplifying this equation to solve for \( M \):
\(\frac{300 \times 100}{M} = \frac{225 \times 100}{M} + 10\)
Clearing the fractions yields:
\(30000 = 22500 + 10M\)
Solving for \( M \):
\(30000 - 22500 = 10M\)
\(7500 = 10M\)
Dividing both sides by 10:
\(M = 750\)
Therefore, the maximum marks are \( 750 \).