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What I tried:

1st phase of voting:

Valid votes=900;invalid votes=100

Let no. of people who voted for(supporters)=x

Let no. of people who voted against(opponents) =y

2nd phase of voting:

Valid votes=800;invalid votes=200

The new number of opponents=$\frac{3}{2}y$, which is now a majority.

Which is equal to$=x(1+\frac{300}{100})=4x$ $$ 4x=\frac{3}{2}y$$ $$\frac{x}{y}=\frac{3}{8}$$

Which seems to contradict the statements.

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I took the statement to mean that the margin for rejection in the second vote was $300\%$ more than the margin for acceptance in the first vote.

Thus if $y$ initially were against, then $900-y$ were initially for. The motion passed by a margin of $(900-y)-y=900-2y$.

In the second vote, $1.5y$ voted against, and $800-1.5y$ voted for. The motion failed by a margin of $1.5y-(800-1.5y)=3y-800$.

So $3y-800=4(900-2y)$.

This gives $y= 400$.

Initial vote: Against $400$; For $500$.

Second vote: Against $600$; For $200$.

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  • $\begingroup$ Sir, so the answer is 600?... $\endgroup$ – Soumee Oct 17 '17 at 19:08

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