Question

In a survey, it was found that 70% people liked to drink milk, 85% liked coffee and 90% liked tea. If n% liked all the three beverages, then the minimum value of ‘n’ is

Answer 1

In a survey, it was found that 70% people liked to drink milk, 85% liked coffee and 90% liked tea.

To find : the minimum value of n if n% liked all the three beverages.

solution : n(milk) = 70 % , n(coffee) = 85% and n(tea) = 90%

we know, n(A u B) = n(A) + n(B) - n(A n B)

here n(milk u coffee) = 100

so, n(milk n coffee) = 70 + 85 - 100 = 55

similarly, n(coffee n tea) = 85 + 90 - 100 = 75

n(tea n milk) = 90 + 70 - 100 = 60

now using formula,

n(A u B u C) = n(A) + n(B) + n(C) - n(A n B) - n(B n C) - n(C n A) + n(A n B n C)

here n(A n B n C) = percentage of people liked all the three beverages.

here n(A u B u C) = 100

100 = 70 + 85 + 90 - 55 - 75 - 60 + n(A n B n C)

⇒100 = 55 + n(A n B n C)

⇒n(A n B n C) = 45

Therefore 45% people liked all three beverages.