A survey of n people in the town 1 found that 50% of them preferred Brand A. Another survey of 100 people in the town 2 found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?

• 50% of n people from town 1 prefer brand A.
  =>50% of n is (50/100) x n = n/2
  
  60% of 100 people from town 2 prefer brand A.
  =>60% of 100 is (60/100) x 100 = 60
  
  Of the total n+100 people surveyed,n/2 + 60 prefer brand A.
  
  Given that this is 55%, we have
  
  {[n/2]+60/[n+100]} x 100 = 55
  solving that
  (n/2)+ 60 = (11/20)n + 55
  
  subtracting n/2 and 60 from both sides we have
  
  => 0 = 11n/20 –n/2 + 55 – 60
  
  => 0 = n/20 – 5
  
  now adding 5 on both sides we have
  
  => 5 = n/20
  
  multiplying both sides by 20
  
  => n = 20 x 5 = 100
  
  Hence, the total number of people surveyed is n+100 = (100 + 100) = 200
  
  
  total no .of people surveyed is 200
  
• 12 years agoHelpfull: Yes(3) No(1)
• No. of People prefered Brand A in Town A =0.5n
  and in Town B=60
  Now, the equation is (0.5n+60)/n+100=0.55
  Solving this,, we get n=100
  Thus total No. of people surveyed is 100+100=200
• 12 years agoHelpfull: Yes(2) No(1)
• Total persons surveyed = 200
  100 from each town.
  
  If x persons were surveyed in town A, then
  
  (x+100)*0.55 = 0.5x+60
  solvingt it, we get
  x=100
  total =100+100=200 persons.
• 12 years agoHelpfull: Yes(1) No(0)
• .55*(n+100) = 0.5n + 60 hence n=100 and the total would turn out to be= 200.
• 12 years agoHelpfull: Yes(0) No(0)