Question

A shopkeeper increases the price of an article by 25% and then offers a discount of 20%. What is the net percentage change in the price?

• A. 0%
• B. 5% increase
• C. 5% decrease
• D. 10% decrease

Hint:

When percentage increase is followed by a percentage decrease, use: Net \% change = \( a + b + \frac{ab}{100} \)

Answer 1

The Correct Option is A

To solve the problem, we need to determine the net effect of a price increase followed by a discount, both expressed in percentages.

1. Understanding the Concepts:

- Price Increase: An upward change in price, expressed as a percentage of the original price.
- Discount: A reduction applied after the increase, on the increased price.
- Net Change Formula: When an increase of x% is followed by a decrease of y%, the net percentage change is given by: \[ \text{Net \% change} = x - y - \frac{xy}{100} \]

2. Given Values:

- Increase = 25%
- Discount = 20%

3. Calculating the Net Percentage Change:

\[ \text{Net \% change} = 25 - 20 - \frac{25 \times 20}{100} = 5 - 5 = 0\% \]

Final Answer:

There is no net change in the price; the overall percentage change is 0%.