Question : If $6A=11B=7C$, then find $A:B:C$.
Option 1: $66:42:77$
Option 2: $77:42:66$
Option 3: $43:77:66$
Option 4: $7:11:6$
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Correct Answer: $77:42:66$
Solution :
Given: $6A=11B=7C$
Let $6A=11B=7C=k$
$⇒A=\frac{k}{6},B=\frac{k}{11},C=\frac{k}{7}$
Ratio of $A:B:C=\frac{k}{6}:\frac{k}{11}:\frac{k}{7}$
$⇒A:B:C=\frac{1}{6}:\frac{1}{11}:\frac{1}{7}$
LCM of $(6, 11, 7) = 462$
Multiplying with it, we get:
$⇒A:B:C=\frac{462}{6}:\frac{462}{11}:\frac{462}{7}$
$\therefore A:B:C = 77:42:66$
Hence, the correct answer is $77:42:66$.
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