If $\frac{1}{a};\frac{1}{b}:\frac{1}{c}=3:4:2$, then determine $a:b:c$.

$4:3:6$

The correct answer is Option (2) → $4:3:6$

1. Identify the relationship

We are given that:

$\frac{1}{a} : \frac{1}{b} : \frac{1}{c} = 3 : 4 : 2$

This means that $a, b,$ and $c$ are proportional to the reciprocals of these numbers:

$a : b : c = \frac{1}{3} : \frac{1}{4} : \frac{1}{2}$

2. Find a common denominator

To convert these fractions into a simple integer ratio, we find the Least Common Multiple (LCM) of the denominators ($3, 4,$ and $2$):

• Multiples of 3: 3, 6, 9, 12, 15...
• Multiples of 4: 4, 8, 12, 16...
• Multiples of 2: 2, 4, 6, 8, 10, 12...

The LCM is 12.

3. Simplify the ratio

Multiply each part of the ratio by the LCM ($12$):

• $a = \frac{1}{3} \times 12 = 4$
• $b = \frac{1}{4} \times 12 = 3$
• $c = \frac{1}{2} \times 12 = 6$

So, the ratio becomes:

$a : b : c = 4 : 3 : 6$

Final Answer: The ratio $a:b:c$ is 4:3:6.