Question

If $a:b=2:3$ and $b:c=9:8$ then the duplicate ratio of $a:c$ is ____

• A. $9:16$
• B. $4:9$
• C. $81:64$
• D. $4:64$

Answer 1

The correct option is A $9:16$

$a:b=2:3$
$b:c=9:8$
$\therefore \frac{a}{b}\times \frac{b}{c}=\frac{2}{3}\times \frac{9}{8}$
$\therefore \frac{a}{c}=\frac{3}{4}\Rightarrow a:c=3:4$.
$\therefore$ The duplicate ratio of $3:4$ is $3^2:4^2=9:16$