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.

You can use inclusion/exclusion but you might not have enough information. Or then again you might.
The number of people who are in  $A$ or $B$ is $A + B - (A\cap B)$ and so if $A+B > 100$ percent we can conclude  $A+B - 100\le A\cap B \le \min (A,B)$
So $WHISKEY + GIN - 100 = 70+60 -100 = 30 \le(WHISKEY \cap GIN) \le \min WHISKEY, GIN = GIN = 60$.
Likewise $TEA + COFFEE - 100 = 90 + 80 100 = 70 \le(COFFEE \cap TEA)\le \min COFFEE, TEA = COFFEE = 80$.
Let $A = (COFFEE \cap TEA)$ and $B = (WHISKEY \cap GIN)$ and $70 + 30 = 100 \le A + B$ so $A+B -100 \le A\cap B$.  But we know that $A \cap B = COFFEE \cap TEA \cap WHISKEY \cap GIN)=0$.  
That can only happen if $A = 70$ and $B = 30$.
So the people drink alcohol $= WHISKEY + GIN - (WHISKEY \cap GIN) = 70 + 60 -30 = 100$ percent.
(We have everybody drinking alcohol and everbody drinking caffeine, and everybody drinks two of one and one of the other:
$30\%$ drink gin, tea, and coffee.
$40\%$ drink whiskey, tea, and coffee.
$10\%$ drink whiskey, gin, and coffee.
$20\%$ drink whiskey, gin, and tea.
