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Answer will be 15.

As given

C1.Smoke-85

C2.Alcohol-75

C3.Smoke as well as tobacco-65

C4.Chewing Gum- 90

Then maximum no. of people who may be addicted to all these=65.

But in  minimal case let the remaining person who does not lie in c1 ,c2 and c4 case  are addicted to few of these four but not to all.

then minimum number of person who is addicted to all=65-(15+25+10)=15
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Now first keep in mind we want to find minimum.

First we abbreviate some terms of questions:

  • Smokers as S
  • Alcohol as A
  • Tobacco as T
  • Chewing Gum as C

So let's start:

  1. We have 85 smokers(S) so 100-85=15 are not smokers.
  2. 75 having alcohol addiction (A) so now if we want to find minimum of S and A then 75-15=60 are both S and A.
  3. 65 is for T, now here we know that if 60 are both S and A then 40 are either S or A. Hence 65-40=25 are S,A and T
  4. Finally 90 is for C so now from point 3 we know that 75 are either S or A or T then 90-75=15 are S,A,T and C is the minimum persons addicted to all 4.  

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