The price of an article is reduced by 25%. In order to retain the original price, the present price has to be increased by

### Concept & Logic Similar to reversing an increase, reversing a percentage *decrease* requires calculating the necessary absolute increase against the *new, smaller base*. If a value decreases by $R\%$, the required percentage increase to return to the original value is given by the formula: $$Increase \% = \frac{R}{100 - R} \times 100$$ ### Step-by-Step Solution * **Initial Setup:** Let the initial price of the article be $100$. * **Applying the Reduction:** The price is reduced by $25\%$. New (Present) Price = $100 - 25 = 75$. * **Calculating the Reversal:** To retain (return to) the original price, the price must go from $75$ back up to $100$. Absolute Increase required = $100 - 75 = 25$. * **Calculating Percentage Increase:** This absolute increase is evaluated against the *present* price base ($75$). Percentage Increase = $(\frac{\text{Absolute Increase}}{\text{Present Price}}) \times 100$ Percentage Increase = $(\frac{25}{75}) \times 100$ Percentage Increase = $(\frac{1}{3}) \times 100 = \frac{100}{3}\%$. * **Converting to Mixed Fraction:** $\frac{100}{3} = 33$ with a remainder of $1$. Result = $33 \frac{1}{3}\%$. ### Exam Strategy & Shortcut Use the fractional change rule for decreases. A $25\%$ reduction is a subtraction of $\frac{1}{4}$. To reverse a subtraction of $\frac{1}{x}$, you must add $\frac{1}{x-1}$. Here, $x = 4$. So we must add $\frac{1}{4-1} = \frac{1}{3}$. The fraction $\frac{1}{3}$ strictly corresponds to $33 \frac{1}{3}\%$. ### Common Pitfall The trap is to select Option B ($25\%$), thinking decreases and increases are symmetrical. Remember that the $25$ unit increase is heavily magnified because it is being calculated over a much smaller starting base ($75$ instead of $100$). ### Final Answer **Therefore, the correct answer is $33 \frac{1}{3}\%$.**