Find the compounded ratio of $(2 : 3)$, $(5 : 7)$ and $(4 : 9)$.

**Principle.** Compounded ratio of $(a : b), (c : d), (e : f)$ is $(ace : bdf)$ — multiply antecedents together, multiply consequents together. **Compute.** Antecedents: $2 \times 5 \times 4 = 40$. Consequents: $3 \times 7 \times 9 = 189$. So the ratio is $40 : 189$ (already in lowest terms since $\gcd(40, 189) = 1$). **Why option D (60 : 189) is wrong.** It miscounts the antecedent product ($2 \times 3 \times 5$ for example) — keep the antecedents and consequents in separate columns.