Question
A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
Answer: Option C
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Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.
Quantity of water in new mixture = \(\left(3-\frac{3x}{8}+x\right) liters\)
Quantity of syrup in new mixture = \(\left(5-\frac{5x}{8}\right) liters\)
So, \(\left(3-\frac{3x}{8}+x\right)=\left(5-\frac{5x}{8}\right)\)
5x + 24 = 40 - 5x
10x = 16
x = \(\frac{8}{5}\)
So, part of the mixture replaced = \(\left(\frac{8}{5}\times\frac{1}{8}\right)=\frac{1}{5}\)
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