x, y, z, u are real numbers such that x : y = y : z = z : u and x : u = 64 : 27. value of x : z is -

$$\eqalign{ & {\text{Let}}\,\frac{x}{y} = \frac{y}{z} = \frac{z}{u} = k. \cr & {\text{Now, }}\frac{x}{u} = \frac{{64}}{{27}} \cr & \Rightarrow \frac{x}{y} \times \frac{y}{z} \times \frac{z}{u} = \frac{{64}}{{27}} \cr & \Rightarrow {k^3} = {\left( {\frac{4}{3}} \right)^3} \cr & \Rightarrow k = \frac{4}{3}. \cr & {\text{So}},\,x:y = y:z = z:u = 4:3. \cr & \therefore \frac{x}{z} = \frac{x}{y} \times \frac{y}{z} = \frac{4}{3} \times \frac{4}{3} = \frac{{16}}{{9.}} \cr} $$