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According to a survey conducted in two cities, A and B, 64% [#permalink]

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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?

Re: According to a survey conducted in two cities, A and B, 64% [#permalink]

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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,

Re: According to a survey conducted in two cities, A and B, 64% [#permalink]

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01 Dec 2014, 10:53

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Re: According to a survey conducted in two cities, A and B, 64% [#permalink]

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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%

According to a survey conducted in two cities, A and B, 64% [#permalink]

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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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