If the price of an article decreases by `25%`, then to restore its former value by how much percent should the new price be increased?

Options

A. 25
B. 20
C. `33.33`
D. 10

Answer

To solve the problem step by step, we will first understand the situation and then calculate the required percentage increase to restore the original price after a decrease.

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

### Step 2: Calculate the new price after a 25% decrease
A decrease of 25% means that the new price is 75% of the original price. Therefore, we can calculate the new price as follows:
\[ \text{New Price} = P - 0.25P = 0.75P \]

### Step 3: Determine how much we need to increase the new price to restore the original price
To restore the original price \( P \), we need to find out how much we need to increase the new price \( 0.75P \).

Let’s denote the increase needed as \( x \). We can set up the equation:
\[ 0.75P + x = P \]

### Step 4: Solve for \( x \)
Rearranging the equation gives us:
\[ x = P - 0.75P = 0.25P \]

### Step 5: Calculate the percentage increase based on the new price
Now, we need to find the percentage increase based on the new price \( 0.75P \):
\[ \text{Percentage Increase} = \left( \frac{x}{\text{New Price}} \right) \times 100 = \left( \frac{0.25P}{0.75P} \right) \times 100 \]

### Step 6: Simplify the percentage increase
The \( P \) cancels out:
\[ \text{Percentage Increase} = \left( \frac{0.25}{0.75} \right) \times 100 = \left( \frac{1}{3} \right) \times 100 = 33.33\% \]

### Conclusion
To restore the original price after a 25% decrease, the new price must be increased by **33.33%**.