In an examination it is required to get 36% of the aggregate marks to pass. A student gets 198 marks and is declared failed by 36 marks. What is the maximum aggregate marks a student can get?

Concept & Formula The passing mark is the sum of the marks obtained and the marks by which the student failed. Once the passing mark is found, equate it to the passing percentage to find the total marks. $$ \text{Total Marks} = \frac{\text{Marks Obtained} + \text{Failed By Marks}}{\text{Passing Percentage}} $$ Step-by-Step Solution * Given: The student obtained $198$ marks and failed by $36$ marks. * Calculate the total marks required to pass: $198 + 36 = 234$ marks. * Given: The passing requirement is $36\%$ of the aggregate (maximum) marks. * Let the maximum aggregate marks be $x$. * Equation: $36\%$ of $x = 234$. * $0.36x = 234 \Rightarrow x = \frac{234}{0.36}$. * $x = \frac{23400}{36} = 650$. Exam Strategy & Shortcut Passing marks = $198 + 36 = 234$. We know $36\%$ = $234$. $1\%$ = $\frac{234}{36}$. Notice that both are divisible by $18$. $\frac{234}{18} = 13$ and $\frac{36}{18} = 2$. So $1\% = \frac{13}{2} = 6.5$. $100\%$ = $6.5 \times 100 = 650$. Common Pitfall Subtracting the failure margin ($36$ marks) from the obtained marks ($198$) instead of adding it. Remember, if a student fails *by* $36$ marks, they need $36$ *more* marks to reach the passing threshold. Final Answer Therefore, the correct answer is **650**.