If $$\frac{x}{2} = \frac{y}{3} = \frac{z}{4} = $$   $$\frac{{2x - 3y + 5z}}{k}{\text{,}}$$    then the value of k is -

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let }}\frac{x}{2} = \frac{y}{3} = \frac{z}{4} = l \cr & {\text{Then,}} \cr & = x = 2l,y = 3l,z = 4l \cr & \therefore \frac{x}{2} = \frac{{2x - 3y + 5z}}{k} \cr & \Rightarrow \frac{{2l}}{2} = \frac{{2 \times 2l - 3 \times 3l + 5 \times 4l}}{k} \cr & \Rightarrow k = 4 - 9 + 20 = 15 \cr} $$