If the price of an article is decreased by 20%, then to restore its former value by what percent should the new price be increased?

Options

A. 20
B. 25
C. 10
D. `12.5`

Answer

To solve the problem step by step, we can follow these calculations:

1. **Assume the Original Price**: Let's assume the original price of the article is \( P = 100 \).

2. **Calculate the Decreased Price**: Since the price is decreased by 20%, we need to find out how much that is:
\[ \text{Decrease} = 20\% \text{ of } 100 = \frac{20}{100} \times 100 = 20 \]
Now, subtract this decrease from the original price:
\[ \text{New Price} = 100 - 20 = 80 \]

3. **Determine the Increase Needed to Restore the Original Price**: To restore the price back to its original value of 100, we need to find out how much we need to increase the new price of 80:
\[ \text{Increase Required} = 100 - 80 = 20 \]

4. **Calculate the Percentage Increase**: Now, we need to find out what percentage this increase (20) is of the new price (80):
\[ \text{Percentage Increase} = \left(\frac{\text{Increase Required}}{\text{New Price}}\right) \times 100 = \left(\frac{20}{80}\right) \times 100 \]
Simplifying this gives:
\[ \text{Percentage Increase} = \frac{20}{80} \times 100 = \frac{1}{4} \times 100 = 25\% \]

Thus, to restore the original price, the new price should be increased by **25%**.