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

The problem requires calculating the cumulative effect of a percentage price increase followed by a percentage discount.

1. Key Concepts:

- Price Increase: An augmentation of the original price, expressed as a percentage.
- Discount: A reduction applied to the price *after* the increase has been implemented.
- Net Change Formula: For a price increase of x% followed by a decrease of y%, the net percentage change is calculated as: \[ \text{Net \% change} = x - y - \frac{xy}{100} \]

2. Provided Data:

- Percentage Increase = 25%
- Percentage Discount = 20%

3. Net Percentage Change Calculation:

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

Conclusion:

The price experiences no overall change, resulting in a net percentage change of 0%.