Two newspapers A and B are published in a city . it is known that 25% of the city population reads A and 20% reads B while 8% reads both A and B . further , 30% of those who read A but not B look into advertisement and 40% of those who read B but not A also look into advertisements , while 50% of those who read both A and B look into advertisement . then , the percentage of the population who look into advertisements is ? [JEE main 2019]
Answers
Let P(A) and P(B) denote the precentage of city population who reda newspapers A and B.
Then from given data ,we have
P(A)=25%= 1/4,P(B)=20%=1/5
P(A∩B)=8%= 2/25
∴ Percentage of those who read A but not B
P(A∩B)=P(A)−P(A∩B) [see theorem 2 & 3] =1/4−2/25
=17/100
=17%
Similarly,P(A∩B)=P(B)−P(A∩B) =1/5-2/25
=3/25
=12%
If P(C) denotes the percentage of those who look into advertisement , then from the given data we obtain P(C)30%ofP(A∩B)+40% of
P(A∩B)+50ofP(A∩B)
= 2/10×17/100+2/5×3/25+1/2×2/25
= 51+48+40/1000
= 139/1000
=13.9%.
Thus the percentage of population who read an advertisement is 13.9%
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Answer:
Percentage of population who look into advertisement is 13.9%
Step-by-step explanation:
Let the population of city is 100 .
Then, n(A) = 25 , n(B) = 20 and n(AB) = 8
- from venn diagram (Given in attachment)
so, n(A∩ not B ) = 17 and n( not A ∩B) = 12
According , to the question , Percentage of the population who look into advertisement is
= [30/100× n (A∩ not B)] + [40× n( notA∩ B) ] + [50/100× n(A∩B]
= (30/100× 17) + (40/100×12 ) + (50/100×8)
= 5.1 + 4.8 + 4 = 13.9% Answer
