baekhwajeom ipgue sarami manhaseo aneuro deureoganeun de sigani geollyeosseo.

Because 에 is the natural particle for the place where a state exists, and 사람이 많다 is a state: there are many people.

So:

• 백화점 입구에 사람이 많다 = There are many people at the department store entrance.

By contrast, 에서 is more commonly used for where an action happens:

• 백화점 입구에서 기다렸어 = I waited at the department store entrance.

In this sentence, the important idea is many people were at the entrance, so 에 fits well.

Korean often does not mark plural when it is already obvious.

Since 많다 already means to be many, 사람이 많다 naturally means there are many people. You do not need 들.

So:

• 사람이 많다 = there are many people
• 사람들이 많다 = also possible, but usually less necessary here

Using 이/가 is also very natural because it marks 사람 as the subject of 많다.

이/가 is the neutral subject marker, and it is very common when introducing the situation or stating a fact.

• 사람이 많아서 = because there were many people

If you used 사람은, it would often sound more contrastive or topical, like:

• 사람은 많았는데... = As for the people, there were many, but...

So in this sentence, 사람이 is the most natural choice.

Here -아서 gives a reason or cause, similar to because or so.

• 사람이 많아서 = because there were many people / there were many people, so...

It connects the cause to the result:

• Cause: 사람이 많아서
• Result: 안으로 들어가는 데 시간이 걸렸어

So the flow is: There were many people, so it took time to get inside.

안으로 means toward the inside / into the inside. It emphasizes direction.

• 안 = inside
• 안에 = in/inside at a location
• 안으로 = inward, to the inside

Since 들어가다 is a movement verb, 안으로 works very naturally:

• 안으로 들어가다 = go in / enter inside

Compare:

• 안에 있다 = be inside
• 안으로 들어가다 = go inside

So 안으로 highlights movement into the building.

Here 데 is a bound noun used in the pattern V-는 데 시간이 걸리다, which means it takes time to do V.

So:

• 들어가는 데 시간이 걸렸어 = it took time to go in / enter

In this pattern, 데 does not mean a physical place. It refers more to the act/situation of doing something.

A helpful way to think about it is:

• 들어가는 데 = in entering / for getting in

Yes, in standard writing they are different.

1. 들어가는 데

   • 들어가는
     • 데
   • This is the grammar pattern meaning in doing / for doing
   • Correct for this sentence

2. 들어가는데

   • This is usually the connective ending -는데
   • It often means something like and, but, when, or sets background

So here, the intended grammar is:

• 들어가는 데 시간이 걸렸어 = It took time to get in

Not:

• 들어가는데... = while going in... / but going in...

In casual writing, people sometimes do not separate them clearly, but the standard form here is 들어가는 데.

Because the pattern with action verbs is normally V-는 데.

So:

• 들어가다 → 들어가는 데

This does not mean present tense in a strict English sense. It is just the normal form used in this grammar pattern.

If you say 들어간 데, it does not fit this pattern well. It can sound like a different kind of modifier, and it would not be the normal way to say it took time to enter.

So for it takes time to do something, the standard form is:

• 가는 데 시간이 걸리다
• 찾는 데 시간이 걸리다
• 들어가는 데 시간이 걸리다

Because 걸리다 is an intransitive verb in this expression.

Korean says:

• 시간이 걸리다 = time is required / it takes time

So 시간 takes the subject marker 이/가, not the object marker 을/를.

Examples:

• 한 시간 걸렸어 = It took one hour
• 시간이 많이 걸렸어 = It took a lot of time

So 시간이 걸렸어 is the correct structure.

Yes. You could say:

• 백화점 입구에 사람이 많아서 들어가는 데 시간이 걸렸어.

That still sounds natural and means basically the same thing.

Adding 안으로 gives a little more directional emphasis, as if you are specifically focusing on getting inside from the entrance area.

So:

• 들어가는 데 시간이 걸렸어 = it took time to get in
• 안으로 들어가는 데 시간이 걸렸어 = it took time to get inside

The version with 안으로 is slightly more vivid.

걸렸어 is informal, casual speech.

Related forms:

• 걸렸어 = casual
• 걸렸어요 = polite everyday speech
• 걸렸습니다 = formal

So this sentence sounds like something you would say to a friend or in casual conversation. If you want to make it polite, you can say:

• 백화점 입구에 사람이 많아서 안으로 들어가는 데 시간이 걸렸어요.