In a random survey 300 people participated. Out of 300 people who took part in the survey, 60 people enjoy listening to Beatles. 45 people enjoy listening to Michael Jackson and 30 people enjoy listening to Pharell Williams. If 20 people have listened to all three then find the no. of people who have listened only Beatles.

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Solution

The correct option is C 25
Let the no. of people who enjoy listening to Beatles be n(B) = 60
Similarly, the no. of people who enjoy listening to Michael Jackson be n(M) = 45
and the no. of people who enjoy listening to Pharell Williams be = n(P) = 30
Also given that the no. of people who listen to all three i.e. n(B ∩ M ∩ P) = 20
We have to find the no. of people who have listened to only Beatles
Let that no. be x.
then, x = (60-45) + (60-30) - 20
Since, ( Demorgan's law - A - (B∩C) = (A - B) ∩ (A - C) )
So, x = 25

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