Question

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] ​

Answer 1

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 2

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