Mental arithmetic in Mixture and allegation

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A vessel is filled with the liquid,3 parts of which are water and 5 parts syrup,How much of the mixture must be drawn off and replaced with the water ,so that mixture may be half water and half syrup

I have tried:

Totally it contains 8 parts,

3/8 5/8

  1/2

1/8 1/8

Ratio is 1:1,for the mixture to become half,what i am doing mistake,is anyone guide me for the Answer,But the answer is 1/5

what i am doing wrong ?