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Your formulation is not accurate.
To be accurate (and to become a true Math problem), it has to be re-written and re-edited.
My editing is this:
In a survey concerning the smoking habits of consumer it was found that
55% smoke cigarette A, 50% smoke cigarette B,40% smoke cigarette C,
30% smoke cigarettes A and B, 20% smoke cigarettes A and C, 12% smoke cigarettes B and C,
while only 10% smoke all three types of cigarettes. What percentage of the population did not smoke?
The solution is below.
The percentage of those who smoke at least one of the three types of cigarettes is
55 + 50 + 40 - 30 - 20 - 12 + 10 = 93 percents. (*)
Therefore, 7% of the population do not smoke. ANSWER
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The key to the solution is this alternate sum in the left side of (*).
For this formula, see the lessons
- Advanced problems on counting elements in sub-sets of a given finite set
- Challenging problems on counting elements in subsets of a given finite set
in this site.