Q. 84.1( 11 Votes )

In a group of 50

Answer :

Let total number of people n(P) = 50


A number of people who drink Tea n(T) = 30.


A number of people who drink coffee n(C).


n(T–C) = 14


i. how may drink tea and coffee both.


We can see that T is disjoint union of n(T–C) and n (T C).


(If A and B are disjoint then n (A B) = n(A) + n(B))


T = n(T–C) n (T C).


n(T) = n(T–C) + n (T C).


30 = 14 + n (T C).


n(T C) = 16.


16 People drink both coffee and tea.


ii. how many drink coffee but not tea.


We know


n (P) = n(T) + n(C) – n (T C)


Substituting the values we get


50 = 30+n(C) – 16


n(C) = 36.


We can see that T is disjoint union of n(C–T) and n (T C).


(If A and B are disjoint then n (A B) = n(A) + n(B))


C = n(C–T) n (T C).


n(C) = n(C–T) + n (T C).


36 = n(C–T) + 16.


n(C–T) = 20.


20 People drink coffee but not tea.


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