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21 May 2025, 00:35
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Here is the most efficient approach for the replacement question in mixtures if the quantity replaced is the same.
The final concentration = [(X - Y)/X]^n
where
X = initial quantity (or capacity of the container in this question)
Y = replaced quantity (8 liters in this question)
n = number of iterations (2 in this question)
Since the final ratio of water to milk is 9:40, the final concentration is 9/49.
We plug in these values to get
[(X - 8)/X]^2 = 9/49
(X-8)/X = 3/7 [square root taken]
7X - 56 = 3X [Cross multiplied]
4X = 56
X = 14
The final concentration = [(X - Y)/X]^n
where
X = initial quantity (or capacity of the container in this question)
Y = replaced quantity (8 liters in this question)
n = number of iterations (2 in this question)
Since the final ratio of water to milk is 9:40, the final concentration is 9/49.
We plug in these values to get
[(X - 8)/X]^2 = 9/49
(X-8)/X = 3/7 [square root taken]
7X - 56 = 3X [Cross multiplied]
4X = 56
X = 14
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