Which sentence is correct: “Did you manage to finish?” or “Did you managed to finish?”

The correct sentence is: “Did you manage to finish?”

Reason:

When forming a question in the past tense with “did,” the auxiliary verb “did” already indicates the past tense. Therefore, the main verb (“manage” in this case) remains in its base form. Adding “managed” would be grammatically incorrect because it repeats the past tense unnecessarily.

Thus, the correct structure is:
Did + subject + base verb + object?

Example:
Correct: Did you manage to finish?
Incorrect: Did you managed to finish?