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

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.

Yes, there is enough information. Clearly the overlap between whiskey drinkers and gin drinkers is at least $30\%$, being exactly $30\%$ iff $40\%$ drink whiskey but not gin, and $30\%$ drink gin but not whiskey. Similarly at least $70\%$ drink both tea and coffee. Since nobody drinks all four, the number who drink both whiskey and gin is exactly $30\%$, and the number who drink alcohol is $30\% + 30\% + 40\%$, i.e. everybody.

Hint: consider what "Nobody drinks all four beverages" means in terms of the four groups

• People who don't drink tea
• People who don't drink coffee
• People who don't drink whiskey
• People who don't drink gin

and then see how big each of those groups are.