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

Options

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

Answer

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

### Step 1: Write down the ratios
We have the ratios:
- First ratio: \( 2:3 \)
- Second ratio: \( 6:11 \)
- Third ratio: \( 11:2 \)

### Step 2: Multiply the first terms of the ratios
To find the compounded ratio, we multiply the first terms of all the ratios:
\[ 2 \times 6 \times 11 \]
Calculating this gives:
\[ 2 \times 6 = 12 \]
\[ 12 \times 11 = 132 \]
So, the first term of the compounded ratio is \( 132 \).

### Step 3: Multiply the second terms of the ratios
Next, we multiply the second terms of all the ratios:
\[ 3 \times 11 \times 2 \]
Calculating this gives:
\[ 3 \times 11 = 33 \]
\[ 33 \times 2 = 66 \]
So, the second term of the compounded ratio is \( 66 \).

### Step 4: Write the compounded ratio
Now we can write the compounded ratio:
\[ 132:66 \]

### Step 5: Simplify the ratio
To simplify \( 132:66 \), we can divide both terms by their greatest common divisor (GCD). The GCD of \( 132 \) and \( 66 \) is \( 66 \):
\[ \frac{132}{66} : \frac{66}{66} = 2:1 \]

### Final Answer
The compounded ratio of \( (2:3) \), \( (6:11) \), and \( (11:2) \) is:
\[ \boxed{2:1} \]

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