Question

a group of 30 people take either tea or coffee. if 12 people do not take tea and 15 people take coffee, then the number of people who take tea is

Answer 1

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Answer 2

Answer:

The number of the people who take tea is 18.

Step-by-step explanation:

Step 1 of 2

Let the sets T and C indicates the sets of people who like tea and coffee respectively.

And the universal set = U

According to the question,

30 people take either tea or coffee, i.e.,

n(U) = 30 or, n(C∪T) = 30

12 people do not take tea, i.e., n(C - T) = 12

15 people take coffee, i.e., n(C) = 15

Step 2 of 2

To find:- The number of people who take tea, i.e., n(T)

As we know,

⇒ n(C - T) = n(C) - n(C∩T)

⇒ 12 = 15 - n(C∩T)

⇒ n(C∩T) = 15 - 12

⇒ n(C∩T) = 3

Now,

n(C∪T) = n(C) + n(T) - n(C∩T)

⇒ n(T) = n(C∪T) - n(C) + n(C∩T)

Substitute the values of n(C∪T), n(C), and n(C∩T) as follows:

⇒ n(T) = 30 - 15 + 3

⇒ n(T) = 18

Therefore, the number of the people who take tea is 18.

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