Explanation:

- Mean Proportional: The mean proportional (or geometric mean) between two numbers $a$ and $b$ is given by the square root of their product: $\sqrt{a\times b}$. So, the mean proportional between 3.6 and 12.1 is $\sqrt{3.6\times 12.1}=6.6$.

- Third Proportional: Given two numbers $a$ and $b$, the third proportional is a number $c$ such that $a:b=b:c$. Solving $c$, we have $c=\frac{b^2}{a}$. So, the third proportional to 2 and 11 is $\frac{{11}^2}{2}=60.5$.

- Ratio: We need the ratio of the mean proportional and third proportional, which is $6.6:60.5$. Simplifying gives approximately $6:55$.

- Answer Options:

- Option 1: 11 : 36

- Option 2: 36 : 5

- Option 3: 6 : 5

- Option 4: 6 : 55