If the price of a book is first decreased by 25% and then increased by 20%, then the net change in the price will be

Concept & Formula To find the net percentage change when a value is subjected to two successive percentage changes, $a\%$ and $b\%$, we use the effective percentage change formula. A decrease is taken as negative and an increase as positive. $$Net Change = a + b + \frac{a \times b}{100}$$ Step-by-Step Solution * **Given:** First change is a 25% decrease ($a = -25$). Second change is a 20% increase ($b = 20$). * **Calculation:** Substitute the values into the successive percentage formula: $$Net Change = -25 + 20 + \frac{-25 \times 20}{100}$$ $$Net Change = -5 - \frac{500}{100}$$ $$Net Change = -5 - 5 = -10\%$$ The negative sign indicates that the final price has decreased by 10% overall. Exam Strategy & Shortcut Use the fractional multiplier method for faster mental math. A 25% decrease means the price becomes $\frac{3}{4}$ of the original. A 20% increase means the price becomes $\frac{6}{5}$ of the new base. Combined multiplier = $\frac{3}{4} \times \frac{6}{5} = \frac{18}{20} = \frac{9}{10}$. A final fraction of $\frac{9}{10}$ means the new price is 90% of the original, which immediately translates to a 10% decrease. Common Pitfall The most common error is simply adding the percentages directly ($-25\% + 20\% = -5\%$), which leads to incorrectly choosing Option C. Successive percentages compound; the 20% increase is calculated on a much smaller base price, so it doesn't recover as much value as a simple addition suggests. Final Answer **Therefore, the correct answer is 10% decrease.**