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

Options

A. 0.1
B. 0.11
C. `9 1/11%`
D. `11 1/9%`

Answer

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

### Step-by-Step Solution:

1. **Define the Original Price**:
Let the original price of the article be represented as \( P \). For simplicity, we can assume \( P = 100 \) (this makes calculations easier).

**Hint**: Start by defining a variable for the original price to simplify calculations.

2. **Calculate the New Price After 10% Decrease**:
A decrease of 10% means we subtract 10% of \( P \) from \( P \):
\[ \text{New Price} = P - 0.10P = 0.90P \]
Substituting \( P = 100 \):
\[ \text{New Price} = 0.90 \times 100 = 90 \]

**Hint**: To find the new price after a percentage decrease, multiply the original price by \( (1 - \text{decrease percentage}) \).

3. **Determine the Amount Needed to Restore the Original Price**:
To restore the original price of \( P \) (which is 100), we need to find out how much we need to increase the new price (90) to get back to 100:
\[ \text{Increase Required} = P - \text{New Price} = 100 - 90 = 10 \]

**Hint**: Subtract the new price from the original price to find the increase needed.

4. **Calculate the Percentage Increase**:
Now, we need to find out what percentage this increase (10) is of the new price (90):
\[ \text{Percentage Increase} = \left( \frac{\text{Increase Required}}{\text{New Price}} \right) \times 100 = \left( \frac{10}{90} \right) \times 100 \]
Simplifying this:
\[ \text{Percentage Increase} = \frac{10}{90} \times 100 = \frac{1000}{90} \approx 11.11\% \]

**Hint**: To find the percentage increase, divide the increase by the new price and multiply by 100.

### Final Answer:
To restore the original price after a 10% decrease, the new price must be increased by approximately **11.11%**.