Ratio and Proportion

Concept:Compounded ratios are obtained by multiplying all antecedents together and all consequents together, then simplifying.Explanation:Duplicate ratio of $4:5$ is $4^2:5^2 = 16:25$.Triplicate ratio of $1:3$ is $1^3:3^3 = 1:27$.Sub‑duplicate ratio of $81:256$ is $\sqrt{81}:\sqrt{256} = 9:16$.Sub‑triplicate ratio of $125:512$ is $\sqrt[3]{125}:\sqrt[3]{512} = 5:8$.Compounded ratio $= (16 \times 1 \times 9 \times 5) : (25 \times 27 \times 16 \times 8)$.Numerator: $16 \times 1 = 16$, $16 \times 9 = 144$, $144 \times 5 = 720$.Denominator: $25 \times 27 = 675$, $675 \times 16 = 10800$, $10800 \times 8 = 86400$.Ratio $= 720 : 86400 = 1 : 120$.Since $1:120$ does not match any given option, the correct choice is “none”.Answer:Option D: none