Latest Infosys Aptitude Question SOLUTION: 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%

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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

Asked In Infosys Garima (11 years ago)

Solved chaitanya Read Solution (7)

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Read Solution (7) :

chaitanya  (11 years ago)

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).

Is this solution Helpfull? Yes (18) | No (5)  

priyanka  (11 years ago)

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)

Is this solution Helpfull? Yes (8) | No   

Prabhu rao  (11 years ago)

BRAND A
1. 50%(n)
2. 60%(100)=60
3. 55% overall
if n=100
then (50+60)/2=55%

Is this solution Helpfull? Yes (2) | No (9)  

Shafu Gupta  (11 years ago)

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

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phani  (11 years ago)

ans:100

n(50/100)+100(60/100)=55/100(n+100)
==>n=100

Is this solution Helpfull? Yes (1) | No (5)  

Pooja.m.m  (11 years ago)

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

Is this solution Helpfull? Yes (1) | No (2)  

jagan  (11 years ago)

1. 50%(n)
2. 60%(100)=60
3. 55% overall
if n=100
then (50+60)/2=55%
so 100+100=200.

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