Explanation:

- The mean proportional (or geometric mean) between two numbers, $a$ and $b$, is given by $\sqrt{ab}$.

- For 24.2 and 7.2, it is $\sqrt{24.2\times 7.2}=\sqrt{174.24}=13.2$.

- The third proportional of two numbers $a$ and $b$ (assuming the sequence $a:b::b:x$ or $a:b=b:x$) is found using $b^2/a$.

- For 2.8 and 4.2, it is $(4.2\times 4.2)/2.8=6.3$.

- The ratio of these two values, the mean proportional and the third proportional, is $13.2:6.3$, which simplifies to $44:21$.

- Option 4: 44:21 is correct.

Based on this calculation: