In a parliamentary debate, a bill was being passed. 600 votes were cast initially but after some discussion, the opposition to the bill went up by 150%. The bill was then rejected by a majority 2 times as great as that by which it was passed previously. How many people rejected the bill initially?
In a parliamentary debate, a bill was being passed. 600 votes were cast initially but after some discussion, the opposition to the bill went up by 150%. The bill was then rejected by a majority 2 times as great as that by which it was passed previously. How many people rejected the bill initially?
The correct option is D 200
There are totally 600 voters, so after the number of people who initially rejected increases by 150%, it must still be below 600. That is true only for option (d).
Verifying the answer chosen:
Initially,
Against = 200, for = 400. Hence, majority = 400-200 = 200
After discussions,
Against =200+1.5×200=500 , for = 600-500 = 100. Hence, majority = 500-100 = 400, which is twice the initial majority. Thus, this is correct answer.
Alternatively:
There are totally 600 voters. Let number of peole, who were in Against = A, and who were in favour = F. Hence, majority = F - A
F + A = 600
After discussions,
The opposition to the bill went 150% . Aganist = 2.5 A, Favour =600−2.5A
According to given question,
2[600−2.5A]=[600−2A]⇒A=200 and F=400.
There are totally 600 voters, so after the number of people who initially rejected increases by 150%, it must still be below 600. That is true only for option (d).
Verifying the answer chosen:
Initially,
Against = 200, for = 400. Hence, majority = 400-200 = 200
After discussions,
Against =200+1.5×200=500 , for = 600-500 = 100. Hence, majority = 500-100 = 400, which is twice the initial majority. Thus, this is correct answer.
Alternatively:
There are totally 600 voters. Let number of peole, who were in Against = A, and who were in favour = F. Hence, majority = F - A
F + A = 600
After discussions,
The opposition to the bill went 150% . Aganist = 2.5 A, Favour =600−2.5A
According to given question,
2[600−2.5A]=[600−2A]⇒A=200 and F=400.
