What time was it 2011 minutes after the beginning of january 1

Okay! 

Notable things in the problem:
2011 minutes AFTER the beginning of January 1rst. 

12:00AM will be our starting time, because that's when January 1rst begins. 
It'll be a bit easier to work with if we convert the 2011 minutes into hours. 
So take 2011 minutes and divide it by 60 to get the number of hours. 

2011 / 60 = 33 hours and 31 minutes

You wouldn't be able to easily get the exact number of minutes from a calculator. You'll need to use long division. The remainder will be the number of minutes. If you want to check you can multiply the number of hours by 60 and add 31 to the product. If it doesn't equal 2011 minutes then something is amiss. 

12:00 AM 

Since we know this is a 24 hour clock we can subtract 24 from our number of hours. (Just remember that this is the next day) 

12:00 AM with 9 hours and 31 minutes left. 

9:31 AM a day later is our time!