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so we can use " although...will do(would do) ..., do (did) " is that right?
Yes, we can use "although X would do..., Y did..." = although (conditional future),...(simple past).
Note that this is a relatively uncommon verb pairing on the GMAT. Rather than studying/memorizing this rather exceptional structure, you should probably just make sure you understand why all of the other choices have clear verb errors.
(A) past perfect "had been" not justified without a simple past verb--"would take" is not simple past.
(B) Simple past for both verbs, "took" and "was," incorrectly indicates simultaneous events.
(C) "was being born" incorrectly indicates ongoing action; the birth would have been a single discrete event.
(E) "was about to be born" incorrectly looks to the future for an event that is clearly supposed to be in the past.