Three varieties of rice, A, B and C costing ? 6 / kg, ? 9 / kg and ? 12 / kg are mixed together

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Three varieties of rice, A, B and C costing ? 6 / kg, ? 9 /...

Three varieties of rice, $A, B$ and $C$ costing $? 6 / \mathrm{kg}$, $? 9 / \mathrm{kg}$ and $? 12 / \mathrm{kg}$ are mixed together in a certain ratio. The mixture is sold at $66 \frac{2}{3} \%$ profit for $? 15 / \mathrm{kg}$. Of the total of $100 \mathrm{~kg}$ of the mixture, $50 \mathrm{~kg}$ is variety $B$. Find the quantity of variety $A$ (in $\mathrm{kgs}$ ) (A) 15 (B) 25 (C) 20 (D) 10

Key Concepts

Mixture Problems

Mixture problems involve combining two or more items with different characteristics (such as cost, concentration, etc.) to create a new mixture. Solving these problems requires finding the amounts of each component that combine to achieve a specified overall characteristic, such as a target average cost or concentration.

System of Equations

The system of equations is a method in algebra used to solve for unknown variables when there are multiple relationships or constraints between them. In mixture problems, setting up equations based on the total quantities and cost relationships allows us to determine the exact amounts of each component in the mixture.

Weighted Average

The concept of weighted average involves calculating an average value that takes into account the relative sizes (weights) of the different components. In mixture problems, each component (such as different varieties of rice) has its own cost, and the overall average cost of the mixture depends on the proportion of each component present.

Profit Percentage

Profit percentage relates the difference between the selling price and the cost price to the cost price, expressed as a percentage. It is used to determine the cost price when the selling price and the profit margin are known, which is crucial in problems that involve selling a mixture at a given profit.

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