Match List I with List II :

Choose the correct answer from the options given below :

Given,

A.) $$4a=5b$$

or, $$\dfrac{a}{b}=\dfrac{5}{4}=\dfrac{45}{36}$$

$$7b=9c$$

or, $$\dfrac{b}{c}=\dfrac{9}{7}=\dfrac{36}{28}$$

So, $$a:b:c=45:36:28$$

So, option (II) is the correct answer for (A).

B.) $$A=\dfrac{1}{4}B$$ and $$B=\dfrac{1}{2}C$$

or, $$\dfrac{A}{B}=\dfrac{1}{4}$$ and $$\dfrac{B}{C}=\dfrac{1}{2}=\dfrac{4}{8}$$

So, $$A:B:C$$ is equal to $$1:4:8$$

So, option (III) is the correct answer for (B).

C.) $$P:Q:R=2:3:4$$

So, $$P:Q=2:3$$, $$Q:R=3:4$$, $$R:P=4:2$$

So, $$\dfrac{P}{Q}:\dfrac{Q}{R}:\dfrac{R}{P}=\dfrac{2}{3}:\dfrac{3}{4}:\dfrac{4}{2}=8:9:24$$

So, option (IV) is the correct answer for (C).

So, option (I) has to be the correct answer for (D).

So, option D is the correct answer.