If 20% of P = 30% of Q = 1/6 of R, then P: Q : R is equal to:

Options

A. `1:2:4`
B. `5:10:6`
C. `15:10:18`
D. `2:5:8`

Answer

To solve the problem, we need to find the ratio of P, Q, and R given the relationships between them. Let's break it down step by step.

### Step-by-Step Solution:

1. **Set Up the Equations**:
We are given that:
\[ 20\% \text{ of } P = 30\% \text{ of } Q = \frac{1}{6} \text{ of } R \]
Let's denote this common value as \( x \). Therefore, we can write:
\[ 20\% \text{ of } P = x \quad \Rightarrow \quad \frac{20}{100} P = x \quad \Rightarrow \quad P = \frac{x \times 100}{20} = 5x \]

2. **Express Q in terms of x**:
From the second part of the equation:
\[ 30\% \text{ of } Q = x \quad \Rightarrow \quad \frac{30}{100} Q = x \quad \Rightarrow \quad Q = \frac{x \times 100}{30} = \frac{10x}{3} \]

3. **Express R in terms of x**:
From the third part of the equation:
\[ \frac{1}{6} \text{ of } R = x \quad \Rightarrow \quad R = 6x \]

4. **Write the Ratios**:
Now we have:
\[ P = 5x, \quad Q = \frac{10x}{3}, \quad R = 6x \]
To find the ratio \( P : Q : R \), we can express them with a common denominator. The least common multiple of the denominators (1, 3, and 1) is 3. Thus, we multiply each term by 3:
\[ P = 5x \times 3 = 15x, \quad Q = \frac{10x}{3} \times 3 = 10x, \quad R = 6x \times 3 = 18x \]

5. **Final Ratio**:
Therefore, the ratio \( P : Q : R \) becomes:
\[ P : Q : R = 15x : 10x : 18x \]
We can simplify this by dividing each term by \( x \):
\[ P : Q : R = 15 : 10 : 18 \]

### Conclusion:
The final ratio of \( P : Q : R \) is:
\[ \boxed{15 : 10 : 18} \]