I guess the first starting point is to define a battle - because if you're after, you know, "The Battle of the Bulge" or a specific one like that, versus an engagement on Hill 380 or a "regular" kind of skirmish, that changes the scope of the question.

But I think you're asking the wrong question, as far as tank vs tank or tank vs infantry. You're going to find the occasional instance, sure, but you're more likely to see tank and infantry vs tank and infantry.

I've just finished reading Alex Kershaw's Liberator, and before that was Beevor's Ardennes, and they both paint clear pictures of combined arms warfare. The largest tank battle in history was at Kursk (or rather, a series of battles collectively called the Battle of Kursk), but even that had several million infantry, artillery, and necessary support. The tank battles of North Africa, such as Crusader, were as much tank vs anti-tank, or tank and anti-tank vs tank and artillery, or some combination. You wouldn't necessarily see a straight force of tanks fighting tanks, except as part of a larger engagement (for that matter, you wouldn't see straight tanks fighting infantry, either - one or the other would likely have artillery, the infantry would need some kind of anti-tank weapon themselves, such as field guns).

But as I said, it depends on the scope of "battles". I don't think you'll find specific numbers because the war was just so enormous that you wouldn't even know what to count. For instance, a German probing attack on the twin villages in the Ardennes - the captain of the American infantry calls for some tank destroyers, a handful arrive and knock out some of the German tanks, and the Germans withdraw. That's an event that occurred, but does that count as a battle? Would that be tank vs tank and infantry, even if the infantry merely keep their heads down and call for something that can do the job?

And even if you want specific, Proper Noun battles - like Second El Alamein - you'll immediately not find any strictly tank vs tank battles. You'll find sections of the battlefield where an armoured force meets another armoured force, but there would almost certainly have been infantry and artillery and close air support involved in the battle, even if they weren't on that particular section of the battlefield at the time.

I doubt any specific such figure exists. However, even tank destroyer units, those with engaging tanks as their primary focus, would carry a 50/50 split of armor piercing and high explosive. If memory serves, the ratio for tanks was about 1:3.