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 = \(\left(\frac{8}{5}\times\frac{1}{8}\right)=\frac{1}{5}\)