Anil mixes cocoa with sugar in the ratio 3 : 2 to prepare mixture A, and coffee with sugar in the ratio 7 : 3 to prepare mixture B. He combines mixtures A and B in the ratio 2 : 3 to make a new mixture C. If he mixes C with an equal amount of milk to make a drink, then the percentage of sugar in this drink will be2 points17
Question
Anil mixes cocoa with sugar in the ratio 3 : 2 to prepare mixture A, and coffee with sugar in the ratio 7 : 3 to prepare mixture B. He combines mixtures A and B in the ratio 2 : 3 to make a new mixture C. If he mixes C with an equal amount of milk to make a drink, then the percentage of sugar in this drink will be2 points17
Solution
Let's break this down step by step:
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In mixture A, the ratio of cocoa to sugar is 3:2. This means that for every 5 parts of the mixture, 2 parts are sugar. So, the percentage of sugar in mixture A is (2/5)*100 = 40%.
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In mixture B, the ratio of coffee to sugar is 7:3. This means that for every 10 parts of the mixture, 3 parts are sugar. So, the percentage of sugar in mixture B is (3/10)*100 = 30%.
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Anil combines mixtures A and B in the ratio 2:3 to make mixture C. This means that for every 5 parts of mixture C, 2 parts come from mixture A and 3 parts come from mixture B. So, the percentage of sugar in mixture C is (2/5)*40% + (3/5)*30% = 16% + 18% = 34%.
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Anil then mixes mixture C with an equal amount of milk to make a drink. This means that the drink is made up of 50% mixture C and 50% milk. Since milk contains no sugar, the percentage of sugar in the drink is (50% of 34%) = 17%.
So, the percentage of sugar in the final drink is 17%.
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