-지만

-지만 links two clauses that contrast with each other, like "but" or "although" in English.

대조·양보Contrast & concession

Han: The first clause talks about yesterday, so it needs its own past tense (바빴지만); -지만 does not take tense from the other clause.

Examples

이 식당은 음식이 비싸지만 맛있어요.The food at this restaurant is expensive but tasty.

어제는 비가 왔지만 오늘은 날씨가 맑아요.It rained yesterday, but today the weather is clear.

한국어는 어렵지만 정말 재미있어요.Korean is difficult, but it's really fun.

죄송하지만 창문 좀 닫아 주시겠어요?Excuse me, but could you close the window, please?

-지만vs-(으)ㄴ/는데-는데 often just gives background before a question or request, while -지만 marks a clear contrast: 배가 고픈데 밥 먹을까요? (-지만 does not fit here).

-지만vs하지만하지만 starts a new sentence, while -지만 joins two clauses into one: 비싸요. 하지만 맛있어요. = 비싸지만 맛있어요.

A/V+지만

N+(이)지만

비싸다 → 비싸지만, 먹다 → 먹었지만, 학생이다 → 학생이지만

Mark past tense on the first clause as well (-았/었지만): the tense of the second clause does not carry back to the first. 어제는 추웠지만 오늘은 따뜻해요.
Attach -지만 directly to the stem, not to a polite ending: 비싸지만, not 비싸요지만.
With nouns use 이지만 after a consonant (학생이지만); after a vowel speakers usually say 지만 (친구지만).
In set phrases like 죄송하지만 and 실례지만 it softens a request or question rather than showing real contrast.

Wrong: ~~어제는 바쁘지만 오늘은 한가해요.~~

Right: 어제는 바빴지만 오늘은 한가해요.

The first clause talks about yesterday, so it needs its own past tense (바빴지만); -지만 does not take tense from the other clause.

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