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?
A. 1/3
B. 1/4
C. 1/5
D. 1/7
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Lets assume that we take x part of the mixture out, and assuming uniform distribution of water and syrup, we can say out of the x part, 3x/8 was water and 5x/8 was syrup, now on replacing this x part by water, both water and syrup part should become equal, we can form the below equation
Water Part = Syrup part
3 – 3x/8 + x = 5 – 5x/8
x +2x/8 = 2
5x/4 = 2
x = 8/5
initially total quantity was 8(i.e. 3+5), and we should take out 1/5th part out and replace it with water to make both equal.
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1/5 is the answer