Why you think 'need' is more suitable here?
A: How long will it ( ) you to finish you work? B: Give me ten more minutes
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A: How long will it take you to finish you work?
is correct. The basic form is:
it will take you (five hours)
take in this context requires a direct object (you).
However, need as used here is intransitive, so you can't write "it will need you". Instead, you have to write:
How long will you need to finish you work?
The basic form here is:
You will need (five hours)