吃午饭了, should 了 be right after 吃？

Question

I saw this sentence from a text book:

你吃午饭了没有？
Have you had lunch yet?

Does the 了 have to be right after the verb 吃 though?

你吃了午饭没有？ 
Have you had lunch yet? 

I learned that 了 with verb represents tense, only when 了 is with verb. However in the sentence given the 了 is after object of 吃, which is 午饭。

EDIT

1. 吃（Verb) + 了 + 午饭（Noun) = Past tense, Correct.

2. 吃 (Verb) + 午饭（Noun) + 了 = NOT Past tense.

I believe that the text book should've used the first one to indicate the past tense, unless the text book has some error, because it does say something like this.

你吃午饭了没有？ ： PAST TENSE

EDIT 2

As I wrote some comments under, I think I should make an additional edit here again.

There are a lot of articles about the usage of 了 I've read many times since I started learning Chinese.

But I'm not really curious about what 了 works here, but whether the translation of 了 is correct or not because this one looks quite suspicious to me.

I believe it is NOT correct to consider it a completion of a specific action, when 了 is used at the end of the sentence.

I believe it is correct to consider it a completion of a specific action, when 了 is used next to the verb and only next to the verb.

From that understanding, I believe it is NOT correct to translate 你吃午饭了没有 into "Have you eaten lunch?" because 了 is not used next to the verb, rather at the end of the sentence.

Am I right about it? or is there anything I am missing?

Answer 1

First of all, “吃午饭了” is usually used for "someone" to ask "someone" to have a lunch. Besides, it also can be meant that you already ate the lunch.

While "吃了午饭 ” just mean that you already ate the lunch.

Plus, there is no such thing like "吃了午饭没有“ It should be "你吃午饭了吗？” The "吗” is used for asking something.

Answer 2

will, I search both in Baidu(A Chinese Search Engine)

吃了午饭 :12,700,000 answers 吃午饭了 : 8,890,000 answers

But in my way , I think 吃午饭了 is the right answer. It's not about grammar,it's about language habits. PS:sorry for my poor english.

Answer 3

I do disagree with Ling Min Hao in the "correct" way to ask this question. Chinese is very flexible in the way a sentence can be constructed, especially in spoken language. In my humble opinion, all of the following expressions are "correct" and natural in spoken language:

1. 你吃午饭了没有？
2. 你吃了午饭没有？
3. 你午饭吃了没有？
4. 你有没有吃午饭？
5. 你吃午饭了吗？
6. 你吃了午饭吗？
7. 你午饭吃了吗？

And what's more, I'd say putting 你 at the end of 4/5/6/7, though maybe grammatically incorrect, is common in spoken language. It causes no ambiguity whatsoever.

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However, if you want to answer the question, you can only answer

我吃了午饭

but not

我吃午饭了
==> 我（去）吃午饭了
==> 我吃午饭（去）了

because the latter means I'm going to have lunch, as shown in the 2 alternative sentences. If you have to put 了 at the end, add 过 after 吃:

我吃过午饭了

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I think user6065 is right in that Chinese does not have tense. But words like 了/过 does give you the sense that the action is completed, in a way similar to the past tense or past perfect tense.