Question: A survey of n people in the town of Eros found that 50% of them prefer Brand A. Another survey of 100 people in the town of Angie found that 60% prefer Brand A. In total, 55% of all the people surveyed together prefer Brand A. What is the total number of people surveyed?

Posted by: arushi on 30.12.2017

Assume no.of people in eros be x.... so its 50/100 of x---->prefer brand A and no.of people in Angie is 100 (as its given) ...so 60/100 of 100--->60 prefer brand A now it is 50x/100+60=55(x+100)/100...on solving its 200

Total no. of people surveyed = (n+100)

People in town of Eros who prefer brand A = n/2

People in town of Angie who prefer brand A = 100*60/100 = 60

All people who prefer brand A = (n + 100)*55/100

n/2 + 60 = (n+100)*55/100

n +120 = (n+100)*11/10

10n + 1200 = 11n + 1100

n = 100

Total number of people surveyed = n+100 = 100+100 = 200

A weighted average question. Since the given average of 50% and 60% is 55% (right in the middle), it means the number of people surveyed in Eros (n) is same as the number of people surveyed in Angie. So n = 100 Total = 100 + 100 = 200

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