Question

in a group of people 72% drink coffee ,44% drink tea. if each person drinks coffee or tea and if there are 40 persons who drink both then the number of people in the group is?

Answer 1

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.

Answer 2

0.72+0.44=1.16

P=40/1.16=34.4827