270 candidates appeared for an examination, of which 252 passed. The pass percentage is:

### Concept & Formula This is a fundamental percentage calculation based on a part-to-whole relationship. To find the percentage of a subset within a total, divide the subset by the total and multiply by $100$. $$ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 $$ ### Step-by-Step Solution **Given:** * Total candidates appeared (Whole) = $270$ * Candidates passed (Part) = $252$ **Calculation / Deduction:** * Set up the fraction for the pass percentage: $$ \frac{252}{270} \times 100 $$ * Simplify the fraction $\frac{252}{270}$ by finding common divisors. Both end in an even number or zero, and their digits sum to multiples of $9$ ($2+5+2=9$, $2+7+0=9$), so they are divisible by $18$. * Divide numerator and denominator by $18$: $252 \div 18 = 14$ $270 \div 18 = 15$ * The simplified fraction is $\frac{14}{15}$. * Now calculate the percentage: $$ \frac{14}{15} \times 100 $$ * Simplify by dividing $100$ and $15$ by $5$: $$ 14 \times \frac{20}{3} = \frac{280}{3} $$ * Convert the improper fraction to a mixed number: $280 \div 3 = 93$ with a remainder of $1$. * This gives $93\frac{1}{3}\%$. ### Exam Strategy & Shortcut Avoid heavy division by looking at the difference. The total is $270$ and passed is $252$. The number of failed candidates is $270 - 252 = 18$. Now, find the failure percentage: $\frac{18}{270}$. This easily simplifies to $\frac{1}{15}$. The pass percentage is simply $100\% - (\frac{1}{15} \text{ as a percent})$. We know $\frac{1}{15}$ is equivalent to $6\frac{2}{3}\%$. $100\% - 6\frac{2}{3}\% = 93\frac{1}{3}\%$. Working with smaller numbers ($18$ instead of $252$) dramatically increases calculation speed. ### Common Pitfall Students often struggle with reducing large fractions like $\frac{252}{270}$ and resort to long division early on (e.g., dividing $25200$ by $270$), which takes significantly more time and introduces a higher risk of arithmetic errors. ### Final Answer Therefore, the correct answer is **$93\frac{1}{3}\%$**.