Question

in a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least one of the two drinks. how many like both coffee and tea

Answer 1

Let A = Set of people who like cold drinks.

B = Set of people who like hot drinks.

Given

(A ∪ B) = 60 n(A) = 27 n(B) = 42 then;

n(A ∩ B) = n(A) + n(B) - n(A ∪ B)

= 27 + 42 - 60

= 69 - 60 = 9

= 9

Therefore, 9 people like both tea and coffee.

Answer 2

Although a part of your answer is missing,you may be referring to this full question:

In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least one of the two drinks. How many people like both cold drink and hot drink?

Given: In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least one of the two drinks.

To find: Number of people who like both cold drink and hot drink.

Solution: Let the number of people who like cold drink be denoted by n(A) and number of people who like hot drink be denoted by n(B).

n(A) = 27 and n(B) = 42

Since each person likes either hot drink or cold drink, therefore total number of people is denoted by n(A∪B).

n(A∪B) = 60

Let the number of people who like both be denoted by n(A∩B).

Using set theory,

n(A∪B) = n(A) + n(B) - n(A∩B)

=> 60 = 27+42-n(A∩B)

=> n(A∩B) = 27+42-60

=> n(A∩B) = 9

Therefore, 9 people like both cold drinks and hot drinks.