Question

If $x:y=2:3$ and $y:z=2:3$, then $x:z=$
(a) $2:3$
(b) $3:4$
(c) $5:7$
(d) $4:9$

Answer 1

Correct option is D. $4:9$

It is given that, $x:y=2:3$...(i) and $y:z=2:3$...(ii)

From (i), we get,

$\Rightarrow \frac{x}{y}=\frac{2}{3}$

$\Rightarrow y=\frac{3x}{2}$...(iii)

Now,

$\Rightarrow \frac{y}{z}=\frac{2}{3}$

$\Rightarrow y=\frac{2z}{3}$

Putting (iii) in (ii), we get,

$\Rightarrow \frac{3x}{2}=\frac{2z}{3}$

$\Rightarrow \frac{x}{z}=\frac{2}{3}\times \frac{2}{3}=\frac{4}{9}$