Question

3. 250 பேர் கலந்து கொண்ட ஒரு விருந்தில், 220 பேர்
காபியும், 60பேர் தேநீரும் சிலர் இரண்டையும் பருகினர்.
30 பேர் காபி அல்லது தேநீர் இவற்றை அருந்தவில்லை
எனில், காபி (ம) தேநீர் இரண்டையும் பருகியவர்கள்
எத்தனைப்பேர்?
a) 40 b) 50 c)60 d) 70​

Answer 1

English Translation:

At a party of 250 people, 220 people

Coffee, 60 tea and some drank both.

30 people do not drink coffee or tea

Those who drink both coffee and tea

how many

a) 40 b) 50 c) 60 d) 70

Those who drink both coffee and tea are 60.

the correct option is c)

Given:

total number of people n(U) = 250

people who drinks coffee n(C) = 220

people who drinks tea n(T) = 60

To find:

those people who drink both coffee and tea

Solution:

using Venn Diagram, we know that,

n(AUB) = n(A) + n(B) - n(A∩B)   ---------(1)

in the case when people neither drink coffee nor tea,

n(AUB)' = n(U) - n(AUB)   -----------(2)

putting the values in equation (2),

⇒ 30 = 250 - n(CUT)

⇒ n(CUT) = 250 - 30

⇒ n(CUT) = 220

putting the value n(CUT) = 220 in equation (1),

⇒n(CUT) = n(C) + n(T) - n(C∩T)

⇒220 = 220 + 60 - n(C∩T)

⇒n(C∩T) = 220 + 60 - 220

⇒n(C∩T) = 60.

So, those people who drink both coffee and tea =60.

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