A shopkeeper first increased the price of an article by 25% and then by 20%. What is the total percent increase?

Concept & Formula To find the total net percentage change when a value is subjected to two successive percentage changes $a\%$ and $b\%$, use the effective percentage formula: $$Net Change = a + b + \frac{a \times b}{100}$$ Step-by-Step Solution * **Given:** First increase $a = 25$, Second increase $b = 20$. * **Calculation:** Substitute both positive values into the successive percentage formula: $$Net Change = 25 + 20 + \frac{25 \times 20}{100}$$ $$Net Change = 45 + \frac{500}{100}$$ $$Net Change = 45 + 5 = 50\%$$ Exam Strategy & Shortcut Alternatively, use the fractional equivalent multiplier method for faster mental math. $25\% = \frac{1}{4}$ (meaning the multiplier is $\frac{5}{4}$) $20\% = \frac{1}{5}$ (meaning the multiplier is $\frac{6}{5}$) Combined multiplier = $\frac{5}{4} \times \frac{6}{5} = \frac{30}{20} = 1.5$ A multiplier of $1.5$ corresponds exactly to a 50% increase. This method scales beautifully and avoids large multiplications. Common Pitfall Simply adding the percentages together ($25\% + 20\% = 45\%$) is a dangerous trap. Successive percentages compound, meaning the second increase is applied to an already inflated base price, yielding a higher total than simple addition. Final Answer **Therefore, the correct answer is 50%.**