Question

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​

Answer 1

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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