Explanation:

Let’s break down the problem:

- Let the marks of the two students be x and y, with x > y.

- Given: x = y + 22

- Also, x = 55% of (x + y) ? x = 0.55(x + y)

Let’s solve:

- From x = 0.55(x + y):

x = 0.55x + 0.55y

x - 0.55x = 0.55y

0.45x = 0.55y

x/y = 0.55/0.45 = 11/9

So, x = (11/9)y

- From x = y + 22:

(11/9)y = y + 22

(11y - 9y)/9 = 22

2y/9 = 22

2y = 198

y = 99

x = 99 + 22 = 121

Now, let’s check the options:

- Option 1: 121 and 99  

- Diff = 22, and 121/(121+99) = 121/220 = 0.55 Both statements satisfied.

- Option 2: 43 and 21

- Diff = 22, but 43/(43+21) ˜ 0.67 Not matching second condition.

- Option 3: 58 and 36

- Diff = 22, but 58/(58+36) ˜ 0.62 Not matching.

- Option 4: 86 and 64

- Diff = 22, but 86/(86+64) ˜ 0.57 Not matching.

Correct answer:

- 121 and 99 (Option 1)

- Satisfies both conditions.