If $\frac{1}{a};\frac{1}{b}:\frac{1}{c}=3:4:2$, then determine $a:b:c$.
Answer & explanation
Correct answer: option 2
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.