Rice Mixture Ratios for Optimum Blending and Cost Savings

Rice is one of the most consumed grains globally, making it a crucial component in many households and restaurants. One common challenge in managing rice supply is determining the optimal ratios to blend different types of rice to achieve a desired price point. In this article, we explore the method to find the ratio of three types of rice priced at Rs. 10/kg, Rs. 15/kg, and Rs. 40/kg to get a mixture costing Rs. 20/kg. This guide is designed to help businesses and individuals make cost-effective decisions by blending different quality and price points of rice.

Understanding the Problem and Solution

To find the correct ratio of the three different types of rice that must be mixed to get a final price of Rs. 20/kg, we can use the following formula. Let the ratio of the three types of rice be x:y:z where:

x is the quantity of rice at Rs. 10/kg y is the quantity of rice at Rs. 15/kg z is the quantity of rice at Rs. 40/kg

The total cost of the mixture should be Rs. 20 per kg. We can write the following equation:

1 15y 40z 20(x y z)

Step 1: Setting up the Equation

To simplify this equation, let's first distribute the 20 across the terms on the right side:

1 15y 40z 2 20y 20z

Subtract 1, 15y, and 20z from both sides to isolate the variables:

40z - 20z 2 - 1 20y - 15y

Simplify:

20z 1 5y

Divide both sides by 5 to further simplify:

4z 2x y

This is our primary equation, which needs to be solved for the ratio x:y:z.

Case Analysis for Ratios

Let's consider specific cases to find the ratio:

Case 1: x y 1kg

Substituting x and y with 1kg:

2(1) 1 4z

3 4z

Hence, z 3/4 kg

Ratio: x : y : z 1kg : 1kg : 3/4kg or 4 : 4 : 3

Case 2: y z 1kg

Substituting y and z with 1kg:

2x 1 4(1)

2x 1 4

2x 3

x 3/2kg

Ratio: x : y : z 3/2kg : 1kg : 1kg or 3 : 2 : 2

Case 3: z x 1kg

Substituting z and x with 1kg:

2(1) y 4(1)

2 y 4

y 2kg

Ratio: x : y : z 1kg : 2kg : 1kg or 1 : 2 : 1

Conclusion and Practical Application

In summary, the possible ratios to achieve a price of Rs. 20/kg by blending rice of different prices are 4:4:3, 3:2:2, and 1:2:1. This guide not only provides the mathematical solution but also practical case studies that can help in making informed decisions about rice blending.

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