In an examination, 96% of students passed and 500 students failed. How many students did appear at the examination?

### Concept & Logic The total number of students appearing for an exam always represents $100\%$. If we know the percentage of students who passed, we can deduce the percentage who failed. Equating this failure percentage to the given numerical value of failed students unlocks the total count. ### Step-by-Step Solution * **Given**: Passed students = $96\%$. Failed students count = $500$. * **Calculation**: 1. Determine the percentage of students who failed. Total students = $100\%$ Failed $\%$ = $100\% - 96\% = 4\%$ 2. Set up the equation where $4\%$ of total students equals $500$. Let total students be $T$. $$4\% \text{ of } T = 500$$ $$\frac{4}{100} \times T = 500$$ 3. Solve for $T$: $$T = 500 \times \frac{100}{4}$$ $$T = 500 \times 25$$ $$T = 12500$$ ### Exam Strategy & Shortcut Memorize fraction equivalents of common percentages. $4\%$ is equivalent to $\frac{1}{25}$. If $\frac{1}{25}$ of the total equals $500$, then the total is simply $500 \times 25$. You can multiply $5 \times 25 = 125$ and append the two zeros instantly to get $12500$ without writing out an equation. ### Common Pitfall A common error is to mistake the $500$ students as representing the $96\%$ that passed, leading to a miscalculation like $0.96T = 500$. Always carefully align the raw number with its corresponding percentage category (pass with pass, fail with fail). ### Final Answer **Therefore, the correct answer is 12500.**