Hi Krish728,
The 'key' this question is that since we're dealing with a mixture, you cannot simply remove "1 part water" or "1 part syrup" - whatever you remove is a mix of the two ingredients. Your equation assumes that you can 'pour out' pure syrup from the mixture - which you can't.
My explanation (higher up in the thread) assumed that there were 15 liters total, but the same approach can be used if there were 30 liters total:
The prompt tells us to REPLACE some of the existing mixture with pure water (with the goal of turning the new mixture into a 40% syrup mix.
To start, we have 30 total liters -->a mixture that is 16 liters water and 14 liters syrup.
If we pour 1 liter of this mixture into a glass, we would have a liquid that is 14/30 = 7/15 syrup (so a little less than half syrup).
For the mixture to be 30 total liters and 40% syrup, we need the mixture to be 18 liters water and 12 liters syrup. In basic math terms, we need to pour out enough of the mixture that we remove 2 full liters of syrup; when we pour an equivalent amount of water back in, we'll have 30 total liters (and 12 of them will be syrup). Since each liter is 7/15 syrup......
We need to remove (2)(15/7) = 30/7 liters and replace them with 30/7 liters of pure water.
30/7 is a little more than 4 liters (about 4.28 liters). Remember that the prompt talks about the number of "PARTS" that need to be replaced though (not the number of liters) - since you 'doubled' all of the numbers to start off with 30 liters, we then have to reduce the result (by dividing by 2) to get the correct answer. 4.28/2 = 2.14
Final Answer:
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Rich
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