Question

In a group every person drinks either tea or coffee or both. If 72% persons drink tea
and 44% persons drink coffee and if there are 192 persons who drink both tea and
coffee, then find total no. of persons in the group.​

Answer 1

Answer:

Let total number who drink either coffee or tea be P, so

Thinking this in the set theory, we have

72% people drink coffee, let this be set A

44% people drink tea, let this be set B

So, we have the formula

n(A∪B) = Total number of people who drink either coffee or tea

And, we also have

n(A∪B) = n(A) + n(B) - n(A∩B)

n(A) = 72% of P = 0.72P

n(B) = 44% of P = 0.44P

n(A∩B) = 40

Putting them, we get

P = 0.72P + 0.44P - 40

0.16P = 40

P = 250

Therefore, number of people in the group is 250.

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Answer 2

Let total number who drink either coffee or tea be P.

So,

• A = 72% people drink tea
• B = 44% people drink coffee

n(A∪B) = Total number of people who drink either coffee or tea

n(A∪B) = n(A) + n(B) - n(A∩B)

• n(A) = 72% of P = 0.72 P
• n(B) = 44% of P = 0.44 P
• n(A∩B) = 192

Putting the values to the equation,

⇒ P = 0.72 P + 0.44 P - 192

⇒ 0.16 P = 192

⇒ P = 1200

Therefore,

Number of people in the group is 1200.