Which one did you bought?
Which one did you buy?
Is it okay to have two past-tense verbs in one sentence?
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Only the second sentence is grammatically correct:
Which one did you buy?
That's because it's only helping verbs like do that change their form according to the tense you're using. All subsequent verbs are always either infinitives or bare infinitives. Infinitives are the ones that have the infinitive marker to in front of them (e.g to buy) and bare infinitives are infinitives without the to (e.g. buy).
The only time when it's actually possible to have two past-tense verbs in the same clause is when you're using one of the several past perfect tenses in English such as the past perfect tense. For example:
I had never seen anything like that.
Strictly speaking, words like seen are not past-tense verbs. More properly, they're called past participles.
In a sentence it is quite possible to have several clauses in the past tense.
I ate cookies and drank milk.
I heard that Peter ate the cookies.
The cookies that Peter ate were rotten.
In all these examples there two clauses.
Also in English a single verb phrase can be made with a helper verb (or an auxillary verb) or a modal verb
It was eating
It was eaten
It had eaten
It did eat
It could eat
In these structures, the helper verb takes the tense (in my examples the helper verb is in the past tense), and the main verb is either a participle (eating/eaten) or an infinitive (eat). These examples all have one clause
It is not grammatically correct to have, for example
*It was ate.
*It did ate.
In your example
*Which one did you bought.
Is not grammatically correct English, and would never be used. "Which one did you buy." is correct.
"Which one did you bought" is not grammatically correct, but I think it's worth noting that you might actually hear something like that in rare cases. It would most likely be playful speech, and it would usually be an exact-echo of something that was just said. For example:
Someone enters the room and excitedly says "I bought it! I bought it! I bought it!" the response might be "What did you bought?"
That kind of phrasing will crash loudly in the ear of a native English speaker. It will draw a lot of attention to the comment being echoed, or to any other language game being played. In the example above the wordplay emphasizes that you told me THREE times that you bought something - and I STILL have no idea what you're talking about. Or maybe I'm repeating "bought" a fourth time just to be silly. Or both.