In a group of 50 people 30 like drinking tea and 20 like drinking coffee. How many people like to drink only coffee, if all 50 people liked at least one of the beverages and 6 people like neither tea nor coffee?
Explanation:
T = Tea
C = Coffee
n means number
n(T) = 30
n(C) = 20
Universal = 50
n(T U C)' = 6 , T union C complement (people who like to drink neither)
Let n(T Π C) i.e. T intersection C (People who like to drink both) = x
n(T) + n(C) - n(T Π C) + n(T U C)' = 50
30 + 20 - x + 6 = 50
56 - x = 50
- x = 50 - 56
-x = -6
x = 6
Therefore people who like to drink BOTH Tea and Coffee are 6.
People who drink coffee = 20
Thus, People who ONLY drink coffee = 20 - 6 = 14 people
Hence, option 1 is the correct answer.
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By: Amit Kumar