The price of an article has been reduced by 25%. In order to restore the original price, the new price must be increased by

Options

A. a)`11(1)/(9)%`
B. b)`66(2)/(3)%`
C. c)`9(1)/(11)%`
D. d)`33(1)/(3)%`

Explanation

To solve the problem step by step, we need to find out how much the new price must be increased in order to restore the original price after a 25% reduction.

### Step 1: Understand the Original Price
Let’s denote the original price of the article as \( P \).

### Step 2: Calculate the Reduced Price
Since the price has been reduced by 25%, the new price can be calculated as:
\[ \text{New Price} = P - 0.25P = 0.75P \]

### Step 3: Determine the Increase Needed to Restore the Original Price
To find out how much we need to increase the new price (\( 0.75P \)) to get back to the original price (\( P \)), we can set up the equation:
\[ \text{Increase} = P - 0.75P = 0.25P \]

### Step 4: Calculate the Percentage Increase
Now, we need to find out what percentage this increase (\( 0.25P \)) is of the new price (\( 0.75P \)):
\[ \text{Percentage Increase} = \left( \frac{\text{Increase}}{\text{New Price}} \right) \times 100 = \left( \frac{0.25P}{0.75P} \right) \times 100 \]

### Step 5: Simplify the Expression
The \( P \) in the numerator and denominator cancels out:
\[ \text{Percentage Increase} = \left( \frac{0.25}{0.75} \right) \times 100 = \left( \frac{1}{3} \right) \times 100 = 33.33\% \]

### Conclusion
Therefore, to restore the original price after a 25% reduction, the new price must be increased by approximately **33.33%**.