Explanation: In economics, the relationship between the price of a good and the quantity demanded is described by the concept of price elasticity of demand. When the price of a good decreases, the quantity demanded typically increases, and vice versa. This relationship is often inverse and can be quantified using percentage changes.
To understand the problem, let's start with the initial conditions. Suppose the original price of an article is \( P \) and the original quantity demanded is \( Q \). If the price decreases by 75%, the new price is \( 0.25P \) (since 100% - 75% = 25%).
The quantity demanded is inversely proportional to the price. This means that if the price is reduced to 25% of its original value, the quantity demanded will increase by a factor that is the inverse of 0.25, which is 4. Therefore, the new quantity demanded will be 4 times the original quantity, or \( 4Q \).
To find the percentage increase in quantity demanded, we calculate the difference between the new quantity and the original quantity, and then express this difference as a percentage of the original quantity:
\[ \text{Percentage Increase} = \left( \frac{4Q - Q}{Q} \right) \times 100\% = \left( \frac{3Q}{Q} \right) \times 100\% = 300\% \]
Thus, if the price of an article decreases by 75%, the quantity demanded increases by 300%.
This concept is crucial in understanding how changes in price affect consumer behavior and is often tested in various competitive examinations such as UPSC, SSC, banking exams, and MBA entrance exams. It is important to remember the inverse relationship between price and quantity demanded and to apply the correct percentage calculations to determine the impact of price changes on demand.