In the recently concluded referendum in New York,
regarding calling back US troops from Iraq, 600 people
voted on a referendum, but after some discussion, the
opponents increased by 150%. The motion was then
rejected by a majority two times as great as that by
which it was formerly passed. How many people voted
against the initial referendum?
(a) 400
(b) 300
(c) 200
(d) 500
Answers
Given : 600 people voted on a referendum, but after some discussion, the opponents increased by 150%.
The motion was then rejected by a majority two times as great as that by
which it was formerly passed
To Find : How many people voted against the initial referendum?
(a) 400
(b) 300
(c) 200
(d) 500
Solution:
Total = 600
Favour = X
opposition = 600 - X
Majority = X - (600 - X) = 2X - 600
opponents increased by 150%
=> New opposition = 600 - X + (150/100)(600 - X) = 2.5(600 - X)
= 1500 - 2.5X
New Favour = 600 - ( 1500 - 2.5X) = 2.5X - 900
New Majority = 1500 - 2.5X - (2.5X - 900)
= 2400 - 5X
2400 - 5X = 2( 2X - 600)
=> 2400 - 5X = 4X - 1200
=> 9X = 3600
=> X = 400
people voted against the initial referendum
opposition = 600 - X = 600 - 400 = 200
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