800 people were supposed to vote on a resolution, but 1/3rd of the people who had decided to vote for the motion were abducted. However, the opponents of the motion, through some means managed to increase their strength by 100%. The motion was then rejected by a majority, which was 50% of that by which it would have been passed if none of these changes would have occurred. How many people finally voted for the motion and against the motion.
a.200 (for), 400 (against)
b.100 (for) and 200 (against)
c.150 (for), 300 (against)
d.200 (for) and 300 (against)
Let no of people for the motion=F
Let no of people against the motion=A
So, originally
A+F=800
(1/3)F gets abducted. Remains (2/3)F.
A gets increased by 100%. Therefore, no of people against the motion becomes 2A
ATQ we get the following equation:
$2A-\frac{2}{3}F=\frac{50}{100}(F-A)$
=> 15A=7F
We can solve this problem by option verification.
Given that, The motion was then rejected by a majority, which was $50$% of that by which it would have been passed if none of these changes would have occurred. So, Option d can be easily dropped as for votes are not $50$% of the against Votes.
Now, $\dfrac13$rd of the people who had decided to vote for the motion were abducted. Means, people who have vote for the resolution is $\dfrac13$ of the people who are against and rejected the bill. For this condition, we can reject the option b and c as well. Since,
Total Vote $=800$
For $=200$
Abducted $=600$
So, option a satisfies the condition.