Question

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 in-
crease 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)​

Answer 1

Answer : 200 ( for ), 400 ( against )

$\rule{100}2$

Step - By step Explanation :

Let the number of people voting for the motion be ' p '

So, number of people voting against the motion will be ' 800 - p '

But,

after abduction and other some means, the number of people voting for the motion becomes $\sf = \dfrac{2}{3} \times p$

Also,

number of people voting against the motion will be $\sf = ( 800 - p ) + ( 800 + p )$

After solving this equation,  we get,

$\sf = 1600 - 2p$

After this, the number of people voting for the motion becomes :-

$\sf = \dfrac{2}{3} \times p - ( 800 - p )$

In the question, it is stated that the motion was rejected  because the number of people voting against the motion was greater than those of voting for the motion.

Now,

According to Question :

$\sf [2(800 - p) - \dfrac{2}{3}\times p - ( 800 - p )] = \dfrac{50}{100} \times [p-(800-p)]$

$\sf\implies 2 [2(800-p)-\dfrac{2}{3}\times p - (800 - p)]$

$\sf\implies 2 [3(800-p)-\dfrac{2}{3}\times p] =p-(800-p)$

$\sf\implies \dfrac{2[9(800-p)-2p]}{3}=p-(800-p)$

$\sf\implies 18(800 - p)-4p = 3p - 3 ( 800 - p )$

Now,

$\sf\implies 21(800-p) =7p$

$\sf\implies 3(800-p) = p$

$\sf\implies 2400-3p=p$

$\sf\implies 2400 = p + 3p$

$\sf\implies 2400 = 4p$

$\sf\implies p =\dfrac{2400}{4}$

$\sf\therefore p = 600$

But, we have to find for the motion and against the motion ( new one ).

So,

For the motion $\sf = \dfrac{2}{3} \times {p}- (800-p)$

$\sf= 400 - 200$

$\sf = 200$ ------------- ( for the motion )

Against the motion $\sf => 1600 - 2p$

$\sf = 1600 - 1200$

$\sf = 400$ ________________ ( Against the motion )

Hence,

Option ( a ) is correct.

$\rule{200}2$

Answer 2

Step-by-step explanation:

Solve this question Through Option:

Given,

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 (iV) can be esily dropped as for votes are not 50% of the against Votes. Now,

1/3rd of the people who had decided to vote for the motion were abducted. Means, people who have vote for the resolution is 1/3 of the people who are against and rejected the bill. For this condition, we can reject the option (ii) and (iii) as well. As

Total Vote = 800

For = 200

Abducted = 600.

Thus, option (i) satisfy the condition.