Assume that you have just heard of a scandal and you are the
first one to know. You pass it on to
four person in a matter of 30 minutes. Each of these four in
turn passes it to four other persons
in the next 30 minutes and so on.
How long it will take for everybody in the World to get to
know the scandal?
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Answer Posted / guest
Assume that nobody hears it more than once and the
population of the World is approximately 5.6
billions.
Everybody in the World will get to know the scandal in 8 hours.
You came to know of a scandal and you passed it on to 4
persons in 30 minutes. So total (1+4) 5
persons would know about it in 30 minutes.
By the end of one hour, 16 more persons would know about it.
So total of (1+4+16) 21 persons would
know about it in one hour.
Similarly, the other (1+4+16+64) persons would have know
about it in one and a half hours.
(1+4+16+64+256) persons would have know about it in two
hours and so on...
It can be deduced that the terms of the above series are the
power of 4 i.e. 4^0, 4^1, 4^2, 4^3 and
so on upto (2N+1) terms. Also, the last term would be 4^2N
where N is the number of hours.
Sum of the above mentioned series = [4^(2N+1)-1]/3
The sum of the series must be 5.6 billions. Hence, equating
the sum of the series with 5.6
billions, we get N=8 hours.
Scandals travel FAST !!!
| Is This Answer Correct ? | 16 Yes | 2 No |
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