47.5 mins
because 2^9=512
& 2^10=1024 but
total no. of persons=768
i.e 512+256(or 2^8)
so for 9th iteration it is 9*5=45mins
but after that only half persons(512/2=256) are to be
informed which will take 2.5mins(5/2). so
the final answer will be 45+2.5=47.5 mins....

First in an aptitude question students are expected to keep
their eyes open to the terms used in the question. Otherwise
an aptitude paper would be the same as that of a 6th or 7th
standard question paper. The original question here was "the
same person". So the same person tells it to different
couple of people taking 5 mins each. 768 person here, so
768/2=384,384*5=1920 should have been the answer.

Now, supposing its a typical maths question, i.e. assuming
all the above assumptions made in the earlier posted answers
to be true, its a simple GP series which starts from 1, then
2 then 4 then 8 and so on.

So, by the problem,
2^0 + 2^1 + 2^2 +....+ 2^n = 768 (note: the first person has
been counted in the series)

so putting the summation formula for GP
1.(2^(n+1)-1) / (2-1) = 768
=> 2^(n+1) = 769
Now, 2^9 = 512 (leaving 257 behind)
Again, the count of 5 mins will be n number of times cause
the first term, i.e. 2^0 is the first person and he already
knows the secret, so the count will start essentially after
him. So n+1=9 => n=8. And for the remaining 257(actually
256, as the first person is counted in it) will be told in
extra 2.5 mins. So total, 8*5 + 2.5 = 42.5

@Crazyfantaxy
because it is told that the same person is telling that
secret to two new people..and then to two new people..and so
on..so the people who have been told will not be taken into
account...47.5 is therefore correct ans which Harry has given

till now total people knowing secret is
1+2+4+8+16+32+64+128+256=511(approxx) heee..

for next 5 min all 256 people will be telling crap secret to
their next 2 people each.so in 5 minutes
we will have 768 people.time required will be same either
we need 257 people or 512 i.e 5minutes

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