Question

$x,y,z,u$ are real number such that $x:y=y:z=z:u$ and $x:u=64:27$. The value of $x:z$ is

• A. $64:27$
• B. $16:9$
• C. $4:3$
• D. $3:4$

Answer 1

The correct option is B $16:9$

$\frac{x}{y}=\frac{y}{z}=\frac{z}{y}=k$

$\therefore x=yk;y=zk;z=4k....k=$ constant

$\therefore \frac{x}{4}=\frac{64}{27}$

$\therefore \frac{y{k}^2}{z}=\frac{64}{27}$

$\therefore k.k^2=\frac{64}{27}$

$\therefore k=\frac{4}{3}$

$\frac{x}{z}=\frac{yk}{uk}=\frac{y}{u}=\frac{2k^2}{2}=k^2$

$\frac{x}{2}={\left(\frac{4}{3}\right)}^2=\frac{16}{y}$