Correct Answer: $\frac{7}{55}$

Solution : 5 parts water and 11 parts syrup (considering the unit volume of the mixture)
Water = $\frac{5}{16}$ and syrup = $\frac{11}{16}$
Let $x$ amount of liquid is replaced by water.
Water = $\frac{5x}{16}$ and syrup = $\frac{11x}{16}$
According to the question,
$\frac{\frac{11}{16}-\frac{11x}{16}}{\frac{5}{16}+x-\frac{5x}{16}}=\frac{3}{2}$
Or, $\frac{\frac{11}{16}-\frac{11x}{16}}{\frac{5}{16}+\frac{11x}{16}}=\frac{3}{2}$
Or, $\frac{15}{16}+\frac{33x}{16}=\frac{22}{16}-\frac{22x}{16}$
Or, $33x+22x=22-15$
Or, $x=\frac{7}{55}$
Hence, the correct answer is $\frac{7}{55}$.