Sugar prices often fluctuate, affecting the quantity of sugar consumers can purchase with a given amount of money. This article explores the mathematical relationship between price reductions and the quantity of sugar that consumers can buy, using examples to illustrate the underlying principles.

Understanding the Relationship Between Price, Quantity, and Consumer Spending

The relationship between price and quantity is a core concept in economics. When the price of a good decreases, consumers can buy a greater quantity of it with the same amount of money. This is particularly relevant when analyzing the impact of a price drop in items like sugar on consumer behavior and purchasing power.

Solving for the Original and Reduced Prices

Let's consider a specific scenario involving sugar. Suppose the price of sugar decreases by 10%, allowing a consumer to purchase 5 kg more sugar for a fixed amount of Rs 270. We need to determine the difference between the original and the reduced price per kg.

Step-by-Step Analysis

Let ( P ) denote the required actual purchase price per kg of the given sugar. The problem can be formulated as follows:

After a 10% reduction, the new price per kg becomes ( 0.9P ). The consumer can buy 5 kg more sugar for Rs 270 after the price drop. Therefore, the quantity of sugar that can be bought at the original price is ( frac{270}{P} ), and at the reduced price, it is ( frac{270}{0.9P} ). According to the problem:

(frac{270}{0.9P} frac{270}{P} 5)

Multiply through by ( 0.9P ) to eliminate the fractions:

270 243 - 4.5P

Simplify the equation:

27 4.5P

Solve for ( P ):

P 6

So, the original price per kg is Rs 6. After a 10% reduction, the new price is:

0.9 x 6 5.4

The difference between the original and reduced price per kg is:

6 - 5.4 0.6

Thus, the difference between the original and reduced price per kg is Rs 0.6.

Generalizing the Solution

The problem can be generalized as follows:

Let the original price per kg of sugar be ( x ). After a 10% reduction, the new price per kg becomes ( 0.9x ). The quantity of sugar that can be bought at the original price is ( frac{270}{x} ). The quantity of sugar that can be bought at the reduced price is ( frac{270}{0.9x} ). According to the problem:

(frac{270}{0.9x} frac{270}{x} 5)

Multiply through by ( 0.9x ) to eliminate the fractions:

270 243 - 4.5x

Simplify the equation:

27 4.5x

Solve for ( x ):

x 6

So, the original price per kg is Rs 6, and the new price is:

0.9 x 6 5.4

The difference between the original and reduced price per kg is:

6 - 5.4 0.6

Therefore, the difference between the original and reduced price per kg is Rs 0.6.

Conclusion

Understanding the relationship between price changes and quantity purchased can help consumers and businesses make informed decisions. By analyzing these relationships, it becomes clear how even small changes in price can significantly impact purchasing power.

Key Takeaways

The quantity of sugar a consumer can buy increases when the price per kg decreases. The difference between the original and reduced price per kg can be calculated using algebraic expressions and equations. Price reductions can have a profound impact on consumer behavior and purchasing power.

Understanding these principles helps in making better financial decisions and optimizing the use of available resources.