Solution A contains equal amount of alcohol and water in it. It is heated till 50 percent of the water in solution A evaporates. Solution B, whose volume is equal to the reduced volume of water in Solution A, is then added to Solution A and the volume of alcohol in the resultant solution is equal to 12 liters. If solution B contains alcohol and water in the ratio 2:3, how many more liters of water should be added to the resultant solution to increase the concentration of water in the resultant solution to 50 percent?
Question
Solution A contains equal amount of alcohol and water in it. It is heated till 50 percent of the water in solution A evaporates. Solution B, whose volume is equal to the reduced volume of water in Solution A, is then added to Solution A and the volume of alcohol in the resultant solution is equal to 12 liters. If solution B contains alcohol and water in the ratio 2:3, how many more liters of water should be added to the resultant solution to increase the concentration of water in the resultant solution to 50 percent?
Solution
Let's break down the problem step by step:
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Solution A contains equal amounts of alcohol and water. Let's assume this amount to be 'x' liters. So, the total volume of Solution A is 2x liters.
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After heating, 50% of the water in Solution A evaporates. So, the amount of water left in Solution A is 0.5x liters.
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The volume of Solution B is equal to the reduced volume of water in Solution A, which is 0.5x liters.
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Solution B contains alcohol and water in the ratio 2:3. So, in 0.5x liters of Solution B, the volume of alcohol is (2/5)*0.5x = 0.2x liters and the volume of water is (3/5)*0.5x = 0.3x liters.
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The volume of alcohol in the resultant solution (Solution A + Solution B) is 12 liters. This is equal to the sum of the volume of alcohol in Solution A and Solution B, which is x + 0.2x = 1.2x liters. From this, we can find the value of 'x' as 12/1.2 = 10 liters.
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The total volume of the resultant solution is the sum of the volume of alcohol, the remaining water in Solution A, and the volume of Solution B, which is 1.2x + 0.5x + 0.5x = 2.2x = 22 liters.
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To increase the concentration of water in the resultant solution to 50%, the volume of water should be equal to the volume of alcohol, which is 12 liters. The current volume of water in the resultant solution is the remaining water in Solution A plus the water in Solution B, which is 0.5x + 0.3x = 0.8x = 8 liters.
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Therefore, to increase the concentration of water to 50%, we need to add 12 - 8 = 4 more liters of water to the resultant solution.
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