Question

in a group of 60 person 15 drink tea but not coffee 32 drink tea how many drink coffee and tea both how many drink coffee but not tea​

Answer 1

Let A and B be sets of persons who drink tea and coffee respectively.

Then

n(A∪B)=50

n(A−B)=14

n(A)=30.

n(A−B)=14

⇒n(A)−n(A∩B)=14

⇒n(A∩B)

n(A)−14=30−14=16.

Answer 2

Given:

Let T and C be the sets of persons who drink tea and coffee respectively.

Total no of persons, n(TUC) = 60

Total no of person drinks tea but not coffee, n(T-C) = 15

Total no of person drinks tea, n(T) = 32

To Find:

i) Total no of person drinks coffee and tea n(T∩C).

ii) Total no of person drinks coffee but not tea n(C-T).

Solution:

i) We know, n(T-C) = n(T)-n(T∩C)

                          15 = 32 - n(T∩C)

                  n(T∩C) = 32 - 15

                               = 17

ii) We have to find n(C)

                   n(TUC) = n(T) + n(C) - n(T∩C)

                          60 = 32 + n(C) - 17

                           n(C) = 45

Now, For n(C-T) we have the formula

n(C-T) = n(C) - n(T∩C)

           = 45 - 17

            = 28

Therefore, 17 persons drink both tea and coffee and 28 persons drink coffee but not tea.

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