If x : y = 3 : 4 and a : b = 1 : 2, then the value of $$\frac{{2xa + yb}}{{3yb - 4xa}}$$   is

$$\eqalign{ & = \frac{x}{y} = \frac{3}{4}{\text{ and }}\frac{a}{b} = \frac{1}{2} \cr & \Rightarrow \frac{{xa}}{{yb}} = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8} \cr & \frac{{2xa + yb}}{{3yb - 4xa}} \cr & = \frac{{2\left( {\frac{{xa}}{{yb}}} \right) + 1}}{{3 - 4\left( {\frac{{xa}}{{yb}}} \right)}} \cr & = \frac{{2 \times \frac{3}{8} + 1}}{{3 - 4 \times \frac{3}{8}}} \cr & = \frac{7}{4} \times \frac{2}{3} \cr & = \frac{7}{6} \cr} $$