Question

The ratio compound of $2:3$ and sub-duplicate ratio of $4:9$ is __________.

• A. $16:81$
• B. $4:9$
• C. $2:1$
• D. $12:81$

Answer 1

The correct option is B $4:9$

we have to find the ratio compound of $2:3$ and sub-duplicate ratio of $4:9$

The duplicate ratio of $a:b$ is also called compound ratio of $a:b$ and is equal to $a^2:b^2$

Similarly, sub-duplicate ratio of $a:b$ is $\sqrt{a}:\sqrt{b}$

Therefore compound ratio of $2:3=4:9$

Sub-duplicate ratio of $4:9=\sqrt{4}:\sqrt{9}=2:3$

Ratio compound =${\left(\frac{4/9}{2/3}\right)}^2=4:9$