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Find the compounded ratio of $(2 : 3)$, $(5 : 7)$ and $(4 : 9)$.
A$30 : 91$
B$40 : 189$
C$50 : 201$
D$60 : 189$
Answer & Solution
Correct answer: B. $40 : 189$
**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.
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