The price of an article is first increased by ` 20%` and later on it is decreased by `25%` due to reduction in sales. Find the net percentage change in final price of the article.

Options

A. `+20%`
B. `-18%`
C. `+38%`
D. `-10%`

Answer

To solve the problem step by step, we will calculate the price of the article after the increase and the subsequent decrease, and then find the net percentage change.

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

### Step 2: Calculate the Price After the Increase
The price is first increased by \( 20\% \).
- Increase = \( 20\% \) of \( 100 = \frac{20}{100} \times 100 = 20 \).
- New Price after increase = \( 100 + 20 = 120 \).

### Step 3: Calculate the Price After the Decrease
Next, the price is decreased by \( 25\% \).
- Decrease = \( 25\% \) of \( 120 = \frac{25}{100} \times 120 = 30 \).
- New Price after decrease = \( 120 - 30 = 90 \).

### Step 4: Calculate the Net Change in Price
Now, we need to find the net change in price from the original price.
- Original Price = \( 100 \)
- Final Price = \( 90 \)
- Change in Price = \( 90 - 100 = -10 \).

### Step 5: Calculate the Net Percentage Change
To find the net percentage change:
\[ \text{Net Percentage Change} = \left( \frac{\text{Change in Price}}{\text{Original Price}} \right) \times 100 = \left( \frac{-10}{100} \right) \times 100 = -10\%. \]

### Final Answer
The net percentage change in the final price of the article is \( -10\% \).