The compounded ratio of (2 : 3), (6: 11) and (11 :2) is

Options

A. A) 1:2
B. B) 2:1
C. C) 11:24
D. D) 36:121

Answer

To find the compounded ratio of the given ratios (2:3), (6:11), and (11:2), we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratios**: We have three ratios:
- First Ratio: \(2:3\)
- Second Ratio: \(6:11\)
- Third Ratio: \(11:2\)

2. **Convert Ratios to Fraction Form**:
- The first ratio \(2:3\) can be written as \(\frac{2}{3}\).
- The second ratio \(6:11\) can be written as \(\frac{6}{11}\).
- The third ratio \(11:2\) can be written as \(\frac{11}{2}\).

3. **Multiply the Ratios**: To find the compounded ratio, we multiply the fractions:
\[ \frac{2}{3} \times \frac{6}{11} \times \frac{11}{2} \]

4. **Simplify the Multiplication**:
- First, multiply the numerators:
\[ 2 \times 6 \times 11 = 132 \]
- Then, multiply the denominators:
\[ 3 \times 11 \times 2 = 66 \]
- So, we have:
\[ \frac{132}{66} \]

5. **Reduce the Fraction**:
- Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 66:
\[ \frac{132 \div 66}{66 \div 66} = \frac{2}{1} \]

6. **Write the Compounded Ratio**: The compounded ratio is \(2:1\).

### Final Answer:
The compounded ratio of (2:3), (6:11), and (11:2) is \(2:1\).

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