Avessel 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 ?

If we want to have half of water and half of syrup we should have the same amount of those two components.
Firs we have 3 parts of water 5 parts of syrup
If we draw off 1 part of syrup and replaced it with one part of water we will have
water: 3+1=4
syrup:5-1=4
So 1 part of syrup must be drawn off

(6,0) i hope it makes enough sense