Question

. In a group of 50 people, 14 drink fruit juice but not cold drink, 30 drink fruit juiceand each person likes at least one of the 2 drinks. Find(1) how many drink fruit juice and cold drink both? (ii) how many drink cold drink

Answer 1

Answer:

Let’s solve this using a venn diagram.

T = Tea

C = Coffee

n means number

n(T) = 30

n(C) = 20

Universal = 50

n(T U C)' = 6 , T union C complement (people who like to drink neither)

Let n(T Π C) i.e. T intersection C (People who like to drink both) = x

n(T) + n(C) - n(T Π C) + n(T U C)' = 50

30 + 20 - x + 6 = 50

56 - x = 50

- x = 50 - 56

-x = -6

x = 6

Therefore people who like to drink BOTH Tea and Coffee are 6.

People who drink coffee = 20

Thus, People who ONLY drink coffee = 20 - 6 = 14 people

I've attached an image with diagram below for better understanding.

Let’s solve this using a venn diagram.

T = Tea

C = Coffee

n means number

n(T) = 30

n(C) = 20

Universal = 50

n(T U C)' = 6 , T union C complement (people who like to drink neither)

Let n(T Π C) i.e. T intersection C (People who like to drink both) = x

n(T) + n(C) - n(T Π C) + n(T U C)' = 50

30 + 20 - x + 6 = 50

56 - x = 50

- x = 50 - 56

-x = -6

x = 6

Therefore people who like to drink BOTH Tea and Coffee are 6.

People who drink coffee = 20

Thus, People who ONLY drink coffee = 20 - 6 = 14 people

I've attached an image with diagram below for better understanding.