Latest CAT Aptitude Question SOLUTION: 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 p

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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?

Asked In CAT Devendra Marghade (12 years ago)

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chaitanya  (12 years ago)

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

Is this solution Helpfull? Yes (3) | No (1)  

Sanjana Patnaik  (12 years ago)

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

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

Aman  (12 years ago)

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.

Is this solution Helpfull? Yes (1) | No   

tarun bhat  (12 years ago)

.55*(n+100) = 0.5n + 60 hence n=100 and the total would turn out to be= 200.

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