Mathematical Formula For Calculating Reverse Percentage
\[ \text{Original Value} = \frac{\text{Percentage Value}}{\text{Percentage Rate}} \times 100 \]
Example Broken Down With Steps
$$
\text{Given: Final Value = 120, Percentage Increase = 20\%}
$$
$$
\text{Step 1: Add 20% to 100%: } 100 + 20 = 120%
$$
$$
\text{Step 2: Convert 120% to decimal: } \frac{120}{100} = 1.2
$$
$$
\text{Step 3: Divide final value by 1.2: } \frac{120}{1.2} = 100
$$
$$
\text{Result: The original price was 100.}
$$
Further Explained
Example: The final price after a 20% increase is 120. Find the original price.
Steps:
- Add the percentage increase to 100%:
$$ 100 + 20 = 120\% $$ - Convert 120% to a decimal:
$$ \frac{120}{100} = 1.2 $$ - Divide the final price by 1.2:
$$ \frac{120}{1.2} = 100 $$ - Conclusion: The original price was 100.