Question

In a group of 80 people, 37 like cold drinks and 52 like hot drinks and each person likes at least one of the two drinks. Find How many people like both coffee and tea

Answer 1

Answer:

9

Step-by-step explanation:

total(P)=80 people

who liked cold drinks(C)=37

who liked hot drinks(H)=52

each like at least one(A)=80

so who liked both= C+H-A

=>37+52-80

=>89-80

9

Answer 2

Concept:

n(C∪T)=N(C)+N(T)-N(C∩T)

C∩T means C intersection T which means area common between C andT

C∪T means C union t which means area covered by both C and T

Given:

In a group of 80 people, 37 like cold drinks and 52 like hot drinks and each person likes at least one of the two drinks.

Find:

Hoe many people drink both tea and coffee

Solution:

Each person likes atleast on eof the two drinks means,

Universal set=C∪T

Where C= no.of people drinking coffee

T= no. of people drinking tea

n(C)=37

n(T)=52

n(C∪T)=80

n(C∪T)=N(C)+N(T)-N(C∩T)

⇒80=37+52-N(C∩T)

⇒N(C∩T)=89-80

               =9

Therefore, the no of people drinking both tea and coffee is 9

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