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Problem involving two sets

Set


Problems related to two sets



Q. In a survey of community, it was found that 70% liked curd, 60% liked milk, 20% didn't like both and 550 people liked both curd and milk. Then,

  • Find the total no. of people participated in the survey
  • Find the total no. of people who like only curd
  • Represent it in venn-diagram.

Solution:

Let U, C and M represents the set of total people in survey, people who like curd and milk respectively.

Given:   n(C)=70%                n(M)=60%                     n(C∪M)'=20%         n(U)=100%
            n(C∩M)=550
We know, 

n(C∪M)= n(U) - n(C∪M)'

               = 100% - 20%

               = 80%

And,   (C∩M) = n(C)+ n(M)- n(C∪M)

                         =70%+ 60%- 80%

                         = 50%

Let the total no. of people in the survey be x.

According to the question,

                  50% of x = 550

                or, (50/100)*x = 550

                or, 0.5 x = 550

                or, x = 550/0.5

                or, x = 1100

  • Therefore, the total no. of people in tge survey is 1100.

Now,  n०(C)= n(C) -n(C∩M)        [०=only]

                      =70%-50%   

                      =20%

Then,  20%of 110=(20/100)*1100= 22

  • So, 220 poeple in the survey liked curd only.

Venn-diagram: