Question

If 7A = 6B = 12C, what is A : B: C?

• A. 7 : 12 : 14
• B. 12 : 14 : 7
• C. 12 : 7 : 14
• D. 14 : 12 : 7

Answer 1

Answer:

B. 12 : 14 : 7

Given:
$7A = 6B = 12C$

Let the common value be (k).

$7A = k \Rightarrow A = \frac{k}{7}$
$6B = k \Rightarrow B = \frac{k}{6}$
$12C = k \Rightarrow C = \frac{k}{12}$

So,
$A : B : C = \frac{1}{7} : \frac{1}{6} : \frac{1}{12}$

Take LCM of denominators (7, 6, 12 = 84):

$= 12 : 14 : 7$

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A : B : C = 12 : 14 : 7