The Impact of Sugar Price Reduction on Purchasing Power

The reduction in the price of sugar can have a significant impact on the purchasing power of consumers. This article explores how a 10% reduction in the price of sugar affects the amount of sugar one can buy with a given budget. We will also solve specific problems and provide the steps to find the solutions using cost calculation and related algebraic methods.

Introduction to Cost Calculation

When the price of sugar is reduced by 10%, the goal is to determine how much more sugar one can purchase for the same amount of money. We will start by defining some variables and then use algebraic manipulations to find the solution.

Algebraic Method for Cost Calculation

Let the original price of sugar be P per kg. After a 10% reduction, the new price is:

new price P - 0.1P 0.9P

Suppose that with a certain amount of money, one can buy 10 kg of sugar at the original price. The total amount of money spent is:

Total Money 10P

With this total amount of money, one can buy sugar at the new price:

Quantity of sugar that can be bought Total Money / New Price 10P / 0.9P 10 / 0.9 ≈ 11.11 kg

Thus, with the same amount of money, one can now buy approximately 11.11 kg of sugar, which is 1.11 kg more than before the price reduction.

Detailed Problem Solving

Let's solve a more specific case with given monetary values and a step-by-step breakdown:

Given:

Amount A Rs 837 After a 10% reduction, the price per kg of sugar is 9/10 of the original price.

We need to find how much more sugar (in kg) can be bought with the same amount of money:

Step-by-Step Solution

1. Let the original price be p0 and the quantity of sugar be q0.

2. After the price reduction, the new price per kg is:

p (9/10) * p0

3. The new quantity of sugar that can be bought is:

q q0 * (10/9)

4. Given that the new quantity is 10 kg more than the original quantity:

q - q0 6.2 kg

5. Solving for q0:

q 10q0 - 6.2

10q0 - 6.2 9q0 / 10

90q0 - 62 9q0

81q0 62

q0 62 / 81 ≈ 0.767 kg

6. The new quantity q is:

q 10 * 0.767 - 6.2 6.2 kg

7. The new price per kg is:

p A / q 837 / 62 Rs 13.5 per kg

In conclusion, you can now buy approximately 11.11 kg of sugar for the same amount of money that was sufficient to buy 10 kg earlier.

Additional Examples and Algebraic Solutions

1. Given: 10 kg of sugar originally cost Rs 540. After a 10% price reduction, 3 kg of sugar costs Rs 90.

Your task is to find the original price of sugar (R).

1. Let X be the quantity and Y be the rate. We know that:

1XY 540 … (1)

2X3Y 90 … (2)

3. We can write equation (2) as:

0.9XY2.7Y 540

4. Since we already know from equation (1) that XY 540, we can substitute:

0.9 * 540 2.7Y 540

2.7Y 540 - 486

Y 54 / 2.7 20 per kg

2. Let the original rate be 'R'. The original cost of 10 kg of sugar is 10R. After a 10% reduction, the new rate of sugar is 0.9R.

Hence, the number of kg of sugar that can be purchased now is:

10R / 0.9R 11.11 kg

Thus, a 10% reduction in price allows one to buy approximately 1.11 kg more sugar for the same amount of money.

Conclusion

The reduction in the price of sugar has a direct impact on the amount of sugar that can be purchased with a fixed budget. By understanding the cost calculation and applying algebraic methods, one can determine the exact quantity of sugar that can be bought with the same amount of money at different price points. This information can be valuable for consumers and businesses alike, helping them make informed decisions about their purchases.