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According to a survey conducted in two cities, A and B, 64%

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According to a survey conducted in two cities, A and B, 64% [#permalink] New post 01 Nov 2012, 21:57
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According to a survey conducted in two cities, A and B, 64% of the population is happy with the new president. If the ratio of the city A population to the city B population is 3:2 and the percentage of city A residents who are happy with the president is 70%, what percentage of city B population is happy with the president?

(A) 30%
(B) 50%
(C) 25%
(D) 55%
(E) 62%
[Reveal] Spoiler: OA
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Re: According to a survey conducted in two cities, A and B, 64% [#permalink] New post 01 Nov 2012, 23:06
A/B = 3/2 = x suppose
thr for A=3x
B=2x

Total A+B=5x

Now 64% is happy with new presedent, 64%*(5x) =3.2x is happy with new present out of total population of A & B

now 70% of A is happy wid new pres, so 70%*(3x) = 2.1x

Total happy people are 3.2x
so B=3.2x-2.1x=1.1x is happy

Now B's population is 2x
1.1x is 55% of total population of B

so Ans : D
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Re: According to a survey conducted in two cities, A and B, 64% [#permalink] New post 02 Nov 2012, 00:35
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actleader wrote:
According to a survey conducted in two cities, A and B, 64% of the population is happy with the new president. If the ratio of the city A population to the city B population is 3:2 and the percentage of city A residents who are happy with the president is 70%, what percentage of city B population is happy with the president?

(A) 30%
(B) 50%
(C) 25%
(D) 55%
(E) 62%


This is actually a weighted average question. Remember mixture questions?
Simply,

\(5*64 = 3*70 + 2*B\)
=>\(2B = 320-210 =110\)
=>\(B= 55\)

Ans D it is.
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Re: According to a survey conducted in two cities, A and B, 64% [#permalink] New post 01 Dec 2014, 10:53
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Re: According to a survey conducted in two cities, A and B, 64% [#permalink] New post 02 Dec 2014, 02:28
Attachment:
happy.png
happy.png [ 3.78 KiB | Viewed 389 times ]


1. Let population of City B = 100

2. Population of City A would be = 150

3. Total population = 250

4. 64% of total happy = 160

5. 70% of City A are happy\(= \frac{70}{100} * 150 = 105\)

6. Happy in City B = 160-105 = 55%

Answer = D
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Re: According to a survey conducted in two cities, A and B, 64% [#permalink] New post 02 Dec 2014, 09:54
actleader wrote:
According to a survey conducted in two cities, A and B, 64% of the population is happy with the new president. If the ratio of the city A population to the city B population is 3:2 and the percentage of city A residents who are happy with the president is 70%, what percentage of city B population is happy with the president?

(A) 30%
(B) 50%
(C) 25%
(D) 55%
(E) 62%


another method, by picking smart numbers. let total population =500 (because ratio of population of cities A and B is 3:2)
thus city A's population =300, City b's population = 200
also, people who are happy with new president = .64*500 = 320
City A's residents who are happy with the president = .7*300 = 210
thus City B's residents who are happy with the new president = 320-210 =110
thus required percentage =\((\frac{110}{200})*100\)
=55%
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According to a survey conducted in two cities, A and B, 64% [#permalink] New post 26 Dec 2014, 09:50
Undoubtedly, weighted average method is the easiest way- one liner
(3*70+2*x)/(3+2)=64
x=55(%)
Alternatively it can also be done by
considering total population of both the cities is 5(3+2), then City A population will be 3 and city B population will be 2
Now,as it is mentioned in the question 64% of the total population is happy and 70% of city A population is happy
Assume x% of population in city B is happy
So,
70*3+x*2=64*5, this is same as the above expression.
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According to a survey conducted in two cities, A and B, 64%   [#permalink] 26 Dec 2014, 09:50
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