In a group of 300 persons 160 drink tea and 170 drink coffee, 80 of them drink both, the number of persons who drink

Question

In a group of 300 persons 160 drink tea and 170 drink coffee, 80 of them drink both, the number of persons who do not drink either tea or coffee

Answer 1

Given data :
n(U)=300 -{universal set total number of persons}
n(T)=160
n(C)=170
n(T∩C)=80

Venn Diagram (added by Murli):

To Find : n(U)- n(T∪C) -------{who do not drink either}

Solution :

n(T∪C)=n(T)+n(C)-n(T∩C)

  =160+170-80
  =250

Now ,

n(U)- n(T∪C) =300-250

          =50

the number of persons who do not drink either tea or coffee is 50

Answer 2

Given data :
n(U)=300 -{universal set total number of persons}
n(T)=160
n(C)=170
n(T∩C)=80

To Find : n(U)- n(T∪C) -------{who do not drink either}

Solution :

n(T∪C)=n(T)+n(C)-n(T∩C)

  =160+170-80
  =250

Now ,

n(U)- n(T∪C) =300-250

          =50

the number of persons who do not drink either tea or coffee is 50