In a village, $90\%$ of people drink Tea, $80\%$ Coffee, $70\%$ Whiskey, $60\%$ Gin. Nobody drinks all four. What percentage of people drinks alcohol? In a small village $90\%$ of the people drink Tea, $80\%$ Coffee, $70\%$ Whiskey and $60\%$ Gin. Nobody drinks all four beverages. What percentage of people of this village drinks alcohol?


I got this riddle from a relative and first thought it can be solved with the inclusion-, exclusion principle. That the percentage of people who drink alcohol has to be in the range from $70\%$ to $100\%$ is obvious to me

When $T$, $C$, $W$, and $G$ are sets, and I assume a village with $100$ people, then what I am looking for is 
$$\lvert W\cup G\rvert = \lvert W\rvert+\lvert G\rvert-\lvert W\cap G\rvert$$ 
I know that 
$$\lvert T \cap C \cap W \cap G \rvert = 0$$ 
and also the absolute values of the singletons.

But I do not see how this brings me any closer, since I still need to figure out what $\lvert W\cap G\rvert$ is and that looks similar hard at this point

On the way there I also noticed that $\lvert T\cap C\rvert \ge 70$ and similar $\lvert W\cap G\rvert \ge 30$

By now I think there is too little information to solve it precisely.
If you add up the percentages, they come out to $300\%$. This means that the average number of beverages per person is $3$. No one drinks more than that, so no one can drink less than that, either. Since everyone drinks exactly three beverages, everyone has exactly one beverage that they don't drink. So no one doesn't drink both whiskey and gin, i.e. everyone drinks alcohol.
Rephrase the question equivalently:

10% don't drink tea, 20% don't drink coffee, 30% don't drink whiskey, and 40% don't drink gin. This must sum to at least 100% (since nobody doesn't not drink all 4).

Clearly they sum to at most exactly 100%, so the "not-X-drinkers" are disjoint sets, and so everybody drinks at least one of whisky or gin.