Question: What percentage of members from among those who voted for New York in round 1, voted for Beijing in round 2?
Explanation:
Let there be x members in the IOC.
As a member cannot vote if his or her city is in contention, the number of voters in Round 1 (R1) = x – 4
The number of voters in Round 2 (R2) = x – 3 and
The number of voters in Round 3 (R3) = x – 2 – n
Where n is the number of voters who have voted for New York (NY) in R1 and Beijing (B) in R2.
Since x – 3 = 83, we get x – 4 = 82 and x – 2 – n = 75 or n = 9
21 members voted for B in R2. Out of these, 9 voted for NY in R1.
The remaining 12 who voted for B comprised 75% of those who voted for B in R1.
Thus 12/0.75 = 16 members voted for B in R1.
∴ Paris (P) got 82 – 16 – 30 – 12 = 24 votes in R1.
All those who voted for London (L) and P in R1 continued to vote for the same cities in subsequent rounds. Thus, 24 voters of P in R2 had voted for P in R1 too. Also from the given information, 3 voters who had voted for NY in R1 voted for Paris in R2.
Out of the remaining 5 that voted for P in R2, 4 had voted for Beijing in R1 and 1 vote came from the member who represented NY.
In R3, the difference in the votes cast for L and P was 1, i.e. L and P got 37 and 38 votes in some order.
The composition of 75 voters of R3 was as follows:
12 members who had voted for B in R1 and R2 were eligible for voting in R3.
30 and 24 members who voted for L and P in R1 continued to do so in R3.
4 voters of R3, voted for B in R1 and P in R2.
3 voters of R3, voted for NY in R1 and P in R2.
1 member represented NY and 1 represented B.
From given information, 50% of voters of B in R1 i.e. 8 voted for P in R3. So, 8 out of the 12 who voted for B in R1 and R2, voted for London in R3.
The information can be summarised as shown in the table:
Required percentage = 9 12
Hence, option (d).