Explanations:The concept of percentage change in quantity when the price of an article changes is based on the inverse relationship between price and quantity. When the price of an article decreases, the quantity that can be bought with the same amount of money increases. This relationship is often seen in economic principles, particularly in the context of price elasticity of demand.
To understand this concept, let's consider an example. Suppose the original price of an article is \( P \) and the original quantity that can be bought with a certain amount of money is \( Q \). If the price decreases by 75%, the new price is \( 0.25P \). With the same amount of money, the quantity that can now be bought is \( \frac{P}{0.25P} \times Q = 4Q \). This means the quantity has increased by 300% (since \( 4Q - Q = 3Q \), and \( \frac{3Q}{Q} \times 100\% = 300\% \)).
The key to solving this problem is recognizing the inverse relationship between price and quantity. A 75% decrease in price means the new price is 25% of the original price, which allows for four times the original quantity to be bought. This is a 300% increase in quantity.
It is important to note that this relationship assumes that the amount of money spent remains constant. If the amount of money spent changes, the relationship between price and quantity would be different. Additionally, in real-world scenarios, the relationship between price and quantity might not always be perfectly inverse due to factors such as price elasticity of demand, which can vary depending on the product and market conditions.
Understanding this concept is crucial for various competitive exams and real-world applications, such as economics, finance, and business management. It helps in making informed decisions about pricing strategies and consumer behavior.