Question : If 6A = 4B = 9C; what is A : B : C?
Option 1: $6:4:9$
Option 2: $9:4:6$
Option 3: $4:9:6$
Option 4: $6:9:4$
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Correct Answer: $6:9:4$
Solution :
Given: 6A = 4B = 9C
Let 6A = 4B = 9C = $k$
⇒ A = $\frac{k}{6}$, B = $\frac{k}{4}$, and C = $\frac{k}{9}$
⇒ A : B : C = $\frac{k}{6}:\frac{k}{4}:\frac{k}{9}$
LCM of (6, 4, and 9) = 36
= $\frac{k}{6}×36:\frac{k}{4}×36:\frac{k}{9}×36=6:9:4$
⇒ A : B : C = $6 : 9 : 4$
Hence, the correct answer is $6:9:4$.
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