Q. 64.0( 5 Votes )

In a group of 50 persons, 30 like tea, 25 like coffee and 16 like both. How many like

(i) either tea or coffee?

(ii) neither tea nor coffee?

Answer :

Given:


In a group of 50 persons,


-30 like tea


-25 like coffee


-16 like both tea and coffee


To find:


(i) People who like either tea or coffee.


Let us consider,


Total number of people = n(X) = 50


People who like tea = n(T) = 30


People who like coffee = n(C) = 25


People who like both tea and coffee = n(T C) = 16


People who like either tea or coffee = n(T C)


Venn diagram:



Therefore,


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


= 30 + 25 – 16


= 39


Thus, People who like either tea or coffee = 39


(ii) People who like neither tea nor coffee.


People who like neither tea nor coffee = n(X) – n(T C)


= 50 – 39


= 11


Therefore, People who like neither tea nor coffee = 11


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RS Aggarwal - Mathematics