Grammar problem

What are the difference between using 던/은
(Noum-modifying form)

Example(1)
학교에 가던 길이었어요
학교에 간 길이었어요

Both means I was on my way to school right,but what is the slight difference between them?

Example (2)

Someone asks
A: 뭐해?

If other people replies with
(A)식당이 찾아보던 중이야
(B)식당이 찾아보는 중이야
(C)식당이 찾아보고 있어

What actually differs between A,B and C??

Question

Grammar problem

What are the difference between using 던/은
(Noum-modifying form)

Example(1)
학교에 가던 길이었어요
학교에 간 길이었어요

Both means I was on my way to school right,but what is the slight difference between them?

Example (2)

Someone asks
A: 뭐해?

If other people replies with 
(A)식당이 찾아보던 중이야
(B)식당이 찾아보는 중이야
(C)식당이 찾아보고 있어

What actually differs between A,B and C??

Answer

I'm sure you are learning advanced Korean.
We don't use "학교에 간 길이었어요"
I think you mean "학교에 가는 길이었어요."
"던" has meaning of past tense. "이었어요" is also past tense.
So first sentence is more correct. But we use second sentence often when I express or talk to others about my memories in realistic.  
If that sentence is from movie, after 2nd sentence, scene might shift to the story about that way to the school.

Examp (2)
식당을 is right. not 이, because 식당 is object.
 
(B) and (c) is same, that means, now i'm looking for 식당 during this talk.
(A) means I was looking for 식당 just before you talk to me. (with eye contact with other person)

Are you clear?

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