A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another surveyof 100 people in the town of Angie 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?
(A)50
(B)100
(C)150
(D)200
(E)250

• 50% of n people from Eros prefer brand A.
  50% of n is 50/100 x n = n/2.
  60% of 100 people from Angie 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) x100 =55
  Solving the equation
  (n/2+60)/(n+100) x100= 55
  (n/2+60) = 55/100x(n+100)
  (n/2+60) = 11/20n+55
  0 = 11n /20 –n/2+55-60
  Now subtracting n/2 and 60 from both sides
  0=n/20-5
  Adding 5 on both sides
  5=n/20
  n=100
  Hence, the total number of people surveyed is
  
  n+ 100 = 100 + 100
  = 200.
  The answer is (D).
  
  
• 11 years agoHelpfull: Yes(18) No(5)
• Total no of people surveyed is (100+n)
  
  In town eros 0.5n people preferred brand A
  
  In town angie 60 people preferred brand A
  
  Now total no of people who preferred brand A is given as (0.5n+60)
  which is also equal to 55% of total surveyed people ==> 0.55(100+n)
  
  i.e (0.5n+60)=0.55(100+n)
  0.05n=5
  n=5/0.05
  n=100
  
  therefore total no of people surveyed is (100+100)=200 (option D)
• 11 years agoHelpfull: Yes(8) No(0)
• BRAND A
  1. 50%(n)
  2. 60%(100)=60
  3. 55% overall
  if n=100
  then (50+60)/2=55%
• 11 years agoHelpfull: Yes(2) No(9)
• ans) B
  
  no.of people of Eros preffered brand A= n/2
  no.of people of Angie preffered brand A= 60%of 100= 60
  hence total no.of people of preffered brand A = n/2+60
  n/2+60 = 55% of (n+100)
  by computing above eqn n=100
  hence total no.of people surveyed= n+100 =100+100= 200
• 11 years agoHelpfull: Yes(2) No(0)
• ans:100
  
  n(50/100)+100(60/100)=55/100(n+100)
  ==>n=100
• 11 years agoHelpfull: Yes(1) No(5)
• given 55% of surveyed people preffered brand A.
  i,e (50%+60%)/2=55%.
  so n must be 100 to get 50%.
  so B is right ans
• 11 years agoHelpfull: Yes(1) No(2)
• 1. 50%(n)
  2. 60%(100)=60
  3. 55% overall
  if n=100
  then (50+60)/2=55%
  so 100+100=200.
• 11 years agoHelpfull: Yes(1) No(0)