# 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?

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