The enrolment of students in a school increases from $560$ to $581$. What is the percent increase in the enrolment?

### Concept & Formula To find the percentage increase, we calculate the absolute increase in value and divide it by the original (initial) value, then multiply by $100$. $$ \text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100 $$ ### Step-by-Step Solution * **Given:** * Original enrolment = $560$ * New enrolment = $581$ * **Calculation:** * First, find the absolute increase in enrolment: * $581 - 560 = 21$ * Next, apply the percentage increase formula using the original enrolment as the base: * $\text{Percent Increase} = \left( \frac{21}{560} \right) \times 100$ * Simplify the fraction by dividing the numerator and denominator by $7$: * $\text{Percent Increase} = \left( \frac{3}{80} \right) \times 100$ * $\text{Percent Increase} = \frac{300}{80} = \frac{30}{8}$ * $\frac{30}{8} = \frac{15}{4} = 3.75\%$ ### Exam Strategy & Shortcut Use the $1\%$ estimation method to quickly zero in on the answer. $1\%$ of the base ($560$) is $5.6$. We need to reach an increase of $21$. Since $5 \times 4 = 20$, multiplying $5.6 \times 4$ gives $22.4$, which is just over our target of $21$. This means the answer must be slightly less than $4\%$. Looking at the options, $3.75\%$ fits perfectly. ### Common Pitfall The most frequent error is calculating the percentage using the *new* value ($581$) as the denominator instead of the *original* value ($560$). Always base percentage changes on the starting figure. ### Final Answer **Therefore, the correct answer is 3.75%.**