A candidate has to obtain minimum $33\%$ of the total marks to pass. He got $25\%$ of the total marks and failed by $40$ marks. The maximum marks are

### Concept & Logic The core logic here is that the difference between the passing percentage and the obtained percentage represents the marks by which the student failed. $$ \text{Pass Percentage} - \text{Obtained Percentage} = \text{Marks Failed By} $$ ### Step-by-Step Solution * **Given:** * Minimum passing percentage = $33\%$ * Candidate's obtained percentage = $25\%$ * Deficit (marks failed by) = $40$ * **Deduction:** * The difference in percentage between what was required and what was obtained is: $33\% - 25\% = 8\%$ * This $8\%$ deficit is exactly equal to the $40$ marks by which the candidate failed. * Let the maximum marks be $x$. * $8\%$ of $x = 40$ * $0.08x = 40$ * $x = \frac{40}{0.08} = 500$ ### Exam Strategy & Shortcut Use the unitary method directly on the percentages. If $8\% = 40$ marks, then dividing both sides by 8 gives: $1\% = 5$ marks. To find the maximum marks ($100\%$), just multiply by 100: $100\% = 5 \times 100 = 500$ marks. ### Common Pitfall A frequent mistake is to assume the candidate's obtained $25\%$ equals $40$ marks, or trying to calculate $33\%$ of $40$. Always equate the *difference* in percentages to the *difference* in absolute marks. ### Final Answer **Therefore, the correct answer is 500.**