If x : y = 3 : 4, then the value of (4x - y) : (2x + 3y) is = ?

A. 4 : 9

B. 8 : 9

C. 4 : 3

D. 8 : 3

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & x:y = 3:4 \cr & \therefore \frac{x}{y} = \frac{3}{4} \cr & \Rightarrow \frac{{4x - y}}{{2x + 3y}} \cr & \Rightarrow \frac{{y\left( {4\frac{x}{y} - 1} \right)}}{{y\left( {2\frac{x}{y} + 3} \right)}} \cr & \Rightarrow \frac{{4 \times \frac{3}{4} - 1}}{{2 \times \frac{3}{4} + 3}} \cr & \Rightarrow \frac{{\left( {3 - 1} \right) \times 2}}{{3 + 6}} \cr & \Rightarrow \frac{4}{9} \cr & \Rightarrow 4:9 \cr} $$