The price of an article is decreased by `10%`. To restore it to its former value, the new price must be increased by :

Options

A. `9(1)/(11)%`
B. `10%`
C. `11%`
D. `11(1)/(9)%`

Answer

To solve the problem, we need to determine how much the new price of the article must be increased to restore it to its original price after a 10% decrease.

### Step-by-Step Solution:

1. **Let the original price of the article be \( P \)**.
- This is the price before any decrease.

2. **Calculate the new price after a 10% decrease**:
- A decrease of 10% means the new price is \( P - 0.10P = 0.90P \).
- Therefore, the new price is \( 0.90P \).

3. **Determine the amount needed to restore the new price to the original price**:
- To find the increase needed, we need to restore \( 0.90P \) back to \( P \).
- The difference between the original price and the new price is:
\[ P - 0.90P = 0.10P \]
- This means we need to increase the new price by \( 0.10P \).

4. **Calculate the percentage increase required**:
- The percentage increase is calculated based on the new price \( 0.90P \):
\[ \text{Percentage Increase} = \left(\frac{\text{Increase}}{\text{New Price}}\right) \times 100 = \left(\frac{0.10P}{0.90P}\right) \times 100 \]
- Simplifying this gives:
\[ \text{Percentage Increase} = \left(\frac{0.10}{0.90}\right) \times 100 = \frac{10}{90} \times 100 = \frac{1000}{90} \approx 11.11\% \]

### Final Answer:
To restore the price of the article to its former value, the new price must be increased by approximately **11.11%**.

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