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Answer the following questions based on the information given below:

The year is $2089.$ Beijing, London, New York and Paris are in contention to host the $2096$ Olympics. The eventual winner is determined through several rounds of voting by members of the IOC with each member representing a different city. All four cities in contention are also represented in IOC.

  • In any round of voting, the city receiving the lowest number of votes in that round gets eliminated. The survivor after the last round of voting gets to host the event.
  • A member is allowed to east votes for at most two different cities in all rounds of voting combined. (Hence, a member becomes ineligible to cast vote in a given round if both the cities (s)he voted for in earlier rounds are out of contention in that round of voting).
  • A member is also ineligible to cast a vote in a round of the city (s)he represent is in contention in that round of voting.
  • As long as a member is eligible, (s)he must vote and vote for only one candidate city in any round of voting.
  • The following incomplete table shows the information of cities that received the maximum and minimum votes in different rounds, the number of votes cast in their favour, and the total votes that were cast in those rounds.
Round Total votes cast Maximum votes cast Eliminated
City No. of votes City No. of votes
1   London 30 New York 12
2 83 Paris 32 Beijing 21
3 75        

It is also known that:

  • All those who voted for London and Paris in round $1,$ continued to vote for the same cities in subsequent rounds as long as cities were in contention. $75\%$ of those who voted for Beijing in round $1,$ voted for Beijing in round $2$ as well.
  • Those who voted for New York and Paris in round $1,$ voted either for Beijing or Paris in round $2.$
  • The difference in votes cast for the two contenting cities in the last round was $1.$
  • $50\%$ of those who voted for Beijing in round $1,$ voted for Paris in round $3.$

What percentage of members from among those who voted for Beijing in round $2$ and were eligible to vote in round $3$, voted for London?

  1. $33.33$
  2. $38.10$
  3. $50$
  4. $66.67$
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