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If both rear tires are the same size, your differential will not suffer, but your speedometer may not be accurate and your gear ratios will not be what they were designed to be, so that could cause strain on the transmission ( and clutch, if you have a clutch.)
If the rear tires are not the same size, that would make the differential turn on the straightway as if you were constantly turning a corner.

---I'm sorry but whoever put this answer doesnt know what they were talking about (No offense meant). You'd probably know if they put different size tires on as your truck would be sitting cockeyed. And if the tires are just the same different size than it will NOT do any damage, your speedometer will just be incorrect. The differential and tranny will run exactly the same no matter what size tire you put on, you will just need to recalibrate your speedometer if you want it to be correct (if you dont care and can figure out how fast you're goin, I wouldn't bother).

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Q: Costco put on the wrong size tire on my truck What damage will this do to the truck's differential?
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