In an examination it is required to get $296$ of the total maximum aggregate marks to pass. A student gets $259$ marks and is decided failed. The difference of marks obtained by the student and that required to pass is $5\%$. What are the maximum aggregate marks a student can get?

### Concept & Logic The problem directly states that the absolute difference between the passing marks and the obtained marks corresponds to exactly $5\%$ of the total maximum aggregate marks. $$ \text{Passing Marks} - \text{Obtained Marks} = \text{Percentage Difference of Total} $$ ### Step-by-Step Solution * **Given:** * Passing marks = $296$ * Obtained marks = $259$ * Percentage equivalent of the difference = $5\%$ * **Calculation:** * First, find the absolute difference in marks: $296 - 259 = 37$ marks. * We are given that this difference is equal to $5\%$ of the total maximum marks. * Let the maximum aggregate marks be $x$. * $5\%$ of $x = 37$ * $\frac{5}{100} \times x = 37$ * $x = 37 \times 20 = 740$ ### Exam Strategy & Shortcut Recognize that $5\%$ is equivalent to the fraction $\frac{1}{20}$. If $\frac{1}{20}$ of the total is $37$, simply multiply $37$ by $20$ to get the total $100\%$. $37 \times 2 = 74$, so $37 \times 20 = 740$. This can be done mentally in seconds. ### Common Pitfall Students sometimes overcomplicate by trying to find the passing percentage first. Since you are given the exact value of the $5\%$ margin, you can bypass intermediate steps and solve directly for the $100\%$ total. ### Final Answer **Therefore, the correct answer is 740.**