How to Calculate Price Reduction and Quantity Purchased in Economics

When analyzing economic scenarios, understanding the relationships between price reduction and the quantity of goods one can purchase is a crucial skill. This article will guide you through solving such problems, step by step, using a scenario involving tea.

Scenario: Reduced Price of Tea and Quantity Purchased

A reduction of 10% in the price of tea enables a person to purchase 25 kg more tea for Rs. 22,500. This problem requires us to determine the reduced price per kg of tea.

Given Data:

Total money: Rs. 22,500 Additional quantity of tea: 25 kg Reduction in price: 10%

Step-by-Step Solution:

Define variables: Let the original price be p0 Let the original quantity be q0 Let the price after reduction be p Let the quantity after reduction be q The new price is 90% of the original price: p/p0 9/10 The new quantity is 110% of the original quantity: q/q0 10/9 Calculate the difference in quantity:

q - q0 25 kg

Solve for the original quantity:

Since q/q0 10/9, we have q 10q0 / 9

Use the relationship between the additional quantity and the total quantity:

q - q0 10q0 / 9 - q0 25

Calculate the original quantity:

6/9q0 25 rarr; q0 25 times; 9 / 6 37.5 kg

Calculate the original price:

4500 / q0 4500 / 37.5 120

Calculate the new price:

The new price is 90% of the original price: 0.9 times; 120 108

Verify the new quantity:

4500 / 108 41.67 kg

Calculate the new quantity considering the additional tea:

37.5 25 62.5 kg

Calculate the reduced price per kg:

837 / 62 13.5 per kg

Additional Scenarios

Scenario 1:

Solution: Let the price per kg be 10. After 20% reduction, the price is 8. The difference in the amount of apples purchased would be 4000/8 - 4000/10 16. Solving for x, the reduced price is 8, which corresponds to 50 per kg.

Scenario 2:

Solution: Let the price of the tea per kg be 10. After a reduction of 10%, the price is 9. The difference in the quantity of tea would be 4500/9 - 4500/10 25. Solving for x, the reduced price per kg is 9, which is Rs. 18.

Scenario 3:

Solution: Let the original price be Rs. x/kg. After a reduction of 10%, the new price per kg is 0.9x. The difference in the quantity of tea that can be purchased would be 22500/0.9x - 22500/x 25. Solving for x, we find the reduced price per kg is 18.

By following these examples, you can better understand how to approach similar problems in economics and apply the concepts of price reduction and quantity purchased.