Question

in a city of 50 lakh people 40% live cricket 22% football how many like both the game​

Answer 1

Answer:

Step-by-step explanation:

the total no of people=50,00,000

no of people like cricket =40% of 50,00,000=(40/100)×50,00,000=20,00,000

no of people who like football=22% of 50,00,000=(22/100)×50,00,000=20,00,000=11,00,000

here,assuming that all the 50 lakh people like atleast one of the two sports

we can apply the set theorem

n(AUB)=n(A)+n(B)-n(A∩B),

where n(A) is the number of people who like cricket

           n(B) is the number of people who like football

           n(A∩B) is the number of people who like both cricket and football

here ,finding n(A∩B) will give our required answer

50,00,000=20,00,000+11,00,000-n(A∩B)

n(A∩B)=-19,00,000 which is the no of people who dont like both the games which is not what we expected or what we want

that means the maximum value (A∩B) can have is 11,00,000 which is equal to n(B) considering it as a subset of A

and the min value of (A∩B) is zero

here,we can only find the max and min value of people liking both the games because it is not said whether all the 50 lakh people like atleast one of the sports.

Hope this helps you

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