Out of 500member of a club, 174 drinks red wine, 178 drinks whiskey, 180 drinks beer. Each member drinks at least one drink .the members who drinks whiskey and beer both must drinks red wine also for every five members who drinks at least two types of the drinks,there are three members who drink all three. Find the numbers of members who drinks all three types of drink?
Answers
Given : 500member of a club, 174 drinks red wine, 178 drinks whiskey, 180 drinks beer. Each member drinks at least one drink .
To find : the numbers of members who drinks all three types of drink
Solution:
Total T = 500
Red Wine R = 174
Whiskey W = 178
Beer B = 180
Drink all W ∩ B ∩ R = a ( to be find )
Drink none = 0 ( Each member drinks at least one drink)
members who drinks whiskey and beer both must drinks red wine also
=> W ∩ B = W ∩ B ∩ R = a
T = R + W + B - W ∩ B - B ∩ R - W ∩ R + W ∩ B ∩ R + None
500 = 174 + 178 + 180 - a - B ∩ R - W ∩ R + a + 0
=> B ∩ R + W ∩ R = 32
Drink atleast 2 types
= ( W ∩ B - W ∩ B ∩ R) + (B ∩ R - W ∩ B ∩ R) + (W ∩ R - W ∩ B ∩ R) + W ∩ B ∩ R
= ( a - a) + (B ∩ R - a) + (W ∩ R - a) + a
= B ∩ R + W ∩ R - a
= 32 - a
Drink all three = a
for every five members who drinks at least two types of the drinks,there are three members who drink all three
=> (32 - a)/a = 5/3
=> 96 - 3a = 5a
=> 96 = 8a
=> a = 12
12 numbers of members drinks all three types of drink
Learn More:
50 students of a class like either oranges or grapes or both. 20 of ...
https://brainly.in/question/13834831
Which two-way table contains the same information as the Venn ...
https://brainly.in/question/9475441
125, 100 and 145 students appeared at post graduate examination ...
https://brainly.in/question/13477941