Class

The minimum number of students who love Algebra only is possible only when all those who love Combinatorics love Algebra too. So, in the this case, $a = 65 - 55 = 10$

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Now, for maximum number of students who love Combinatorics only, every student in the class should love atleast one among Combinatorics and Algebra. Now, let the number of students who love both Algebra and Combinatorics be $x$ . Then the number of students who love only Algebra = (65 - x) and those who love only Combinatorics = (55-x).

Now, $(65 - x) + x + (55 - x) = 100$ . (It would sum up to the total number of students in the class because each students loves atleast one topic.)
$120 - x = 100$
$x = 20$

So, those who love only Combinatorics = $55 - x = 55 - 20 = 35$
So, $b = 35$ .

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$\therefore$ $a + b = 10 + 35 = \boxed{45}$