The price of an article is cut by 42%. To restore to its original value, the new price must be increased by

Options

A. 0.42
B. 0.7241
C. 0.2958
D. 0.525

Answer

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

### Step 1: Assume the Original Price
Let's assume the original price of the article is \( P = 100 \) (this makes calculations easier).

**Hint:** Start by assuming a simple value for the original price to simplify calculations.

### Step 2: Calculate the Discount Amount
The price is cut by 42%. Therefore, the discount amount can be calculated as:
\[ \text{Discount} = 42\% \text{ of } 100 = \frac{42}{100} \times 100 = 42 \]

**Hint:** To find the discount, multiply the percentage by the original price.

### Step 3: Calculate the New Price
Now, subtract the discount from the original price to find the new price:
\[ \text{New Price} = 100 - 42 = 58 \]

**Hint:** The new price is found by subtracting the discount from the original price.

### Step 4: Determine the Increase Needed to Restore the Original Price
To restore the original price of 100, we need to find out how much to increase the new price of 58:
\[ \text{Increase Required} = 100 - 58 = 42 \]

**Hint:** The increase required is the difference between the original price and the new price.

### Step 5: Calculate the Percentage Increase
Now, we need to find the percentage increase based on the new price:
\[ \text{Percentage Increase} = \left(\frac{\text{Increase Required}}{\text{New Price}}\right) \times 100 = \left(\frac{42}{58}\right) \times 100 \]

Calculating this gives:
\[ \text{Percentage Increase} = \frac{4200}{58} \approx 72.41 \]

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

### Step 6: Convert Percentage to Decimal
To express the percentage increase as a decimal:
\[ \text{Decimal Increase} = \frac{72.41}{100} = 0.7241 \]

**Hint:** To convert a percentage to a decimal, divide by 100.

### Conclusion
The new price must be increased by approximately \( 0.7241 \) (or 72.41%) to restore it to its original value.

**Final Answer:** The correct option is \( 0.7241 \).