In mixture A, the ratio of coco and sugar is 3:2 and in mixture B, the ratio of coffee and sugar is 7 : 3. These two were mixed together in the ratio 2:3 to make mixture C. Now equal quantities of C and milk are mixed. Find the percentage of sugar in the mixture.
Approach Solution - 1
Let's denote the quantities of cocoa and sugar in mixture A as 3x and 2x respectively, and in mixture B as 7y and 3y respectively.
The ratio of cocoa to sugar in mixture A is 3:2, so we can express the quantities of cocoa and sugar in A as 3x and 2x respectively.
Similarly, the ratio of coffee to sugar in mixture B is 7:3, so we can express the quantities of coffee and sugar in B as 7y and 3y respectively.
Now, the two mixtures A and B are mixed together in the ratio 2:3 to form mixture C. Therefore, the quantities of cocoa and sugar in mixture C are 2(3x)+3(7y)=6x+21y and 2(2x)+3(3y)=4x+9y respectively.
Now, equal quantities of mixture C and milk are mixed. Let z be the common factor for the amounts of sugar in mixture C and milk.
The total quantity of sugar in the final mixture is 4x+9y+z, and the total quantity of the mixture is 6x+21y+2z.
The percentage of sugar in the mixture is given by the formula: Percentage of Sugar=\(\frac{4x+9x}{6x+21y+2x}\)×100
Percentage of Sugar=\(\frac{4x+9x}{6x+21y+2x}\)×100
If the given answer is 17%, then we can set up the equation: \(\frac{4x+9x}{6x+21y+2x}\)×100=17
Hence, the percentage of sugar in the mixture is 17%.
Approach Solution -2
Suppose mixture A has a volume of 200 milliliters. This means that there are 120 milliliters of cocoa and 80 milliliters of sugar in the mixture.
Similarly, if the combination's volume is 300 ml, it means that there are 210 and 90 ml of sugar and coffee in the mixture, respectively.
We now mix mixtures A and B in a 2:3 ratio.
Thus, the amount of sugar is (90+80) = 170 ml, and the volume of mixture C is (200+300) = 500 ml.
In order to produce a drink, he now blends C with an equivalent volume of milk, suggesting that the final mixture will have a volume of (500+500) = 1000 ml. There are 170 milliliters of sugar in the finished mixture.
Therefore, the proportion is 17%.
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