Explanation:

- To solve this, let's assume the marks of the two students are $x$ and $x+22$.

- The sum of their marks is $x+(x+22)=2x+22$.

- According to the problem, $x+22$ is 55% of the total sum:

$(x+22)=0.55\times (2x+22)$.

- Simplifying, we have:

$x+22=1.1x+12.1$.

- Solving this equation results in $x=43$ and $x+22=65$.

- Option 1: 121 and 99

- The difference is 22, but 121 is not 55% of (121 + 99).

- Option 2: 43 and 21

- Incorrect difference of 22 marks.

- Option 3: 58 and 36

- Incorrect difference of 22 marks.

- Option 4: 86 and 64

- The difference is 22.

- $86=0.55\times (86+64)=0.55\times 150=82.5$, but since this does not work, let's correct:

- Correct calculation shows 43 and 65 are the accurate marks based on the solved equation and none exactly fits but solving showed actual numbers.