A mixture of wheat is sold at Rs.3 per Kg. This mixture is formed by mixing the Wheat of Rs.2.10 per kg and Rs.2.52 per kg. What is the ratio of price of cheaper to the costlier quality in the mixture if the profit of 25% is being earned
Question
A mixture of wheat is sold at Rs.3 per Kg. This mixture is formed by mixing the Wheat of Rs.2.10 per kg and Rs.2.52 per kg. What is the ratio of price of cheaper to the costlier quality in the mixture if the profit of 25% is being earned
Solution
Let's denote the quantity of the cheaper wheat as 'x' kg and the quantity of the costlier wheat as 'y' kg.
Given that the selling price of the mixture is Rs.3 per kg and a profit of 25% is being earned, this means that the cost price of the mixture is Rs.3/1.25 = Rs.2.4 per kg.
The cost price of the mixture is also the weighted average of the prices of the cheaper and costlier wheat, weighted by their respective quantities. So, we have:
2.10x + 2.52y = 2.4(x + y)
Solving this equation for y/x gives us the ratio of the quantity of cheaper wheat to the quantity of costlier wheat in the mixture.
Rearranging the equation gives:
2.10x + 2.52y = 2.4x + 2.4y 0.3x = 0.12y
So, y/x = 0.3/0.12 = 2.5
Therefore, the ratio of the price of cheaper to the costlier quality in the mixture is 1:2.5.
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